Technical Report The acquisition of a unification-based generalised categorial grammar Aline Villavicencio

Technical Report The acquisition of a unification-based generalised categorial grammar Aline Villavicencio
Technical Report
UCAM-CL-TR-533
ISSN 1476-2986
Number 533
Computer Laboratory
The acquisition of a unification-based
generalised categorial grammar
Aline Villavicencio
April 2002
JJ Thomson Avenue
Cambridge CB3 0FD
United Kingdom
phone +44 1223 763500
http://www.cl.cam.ac.uk/
c 2002 Aline Villavicencio
This technical report is based on a dissertation submitted
September 2001 by the author for the degree of Doctor of
Philosophy to the University of Cambridge, Hughes Hall.
The thesis was partially sponsored by a doctoral studentship from
CAPES/Brazil.
Technical reports published by the University of Cambridge
Computer Laboratory are freely available via the Internet:
http://www.cl.cam.ac.uk/TechReports/
Series editor: Markus Kuhn
ISSN 1476-2986
To my family
3
Abstract
The purpose of this work is to investigate the process of grammatical acquisition
from data. In order to do that, a computational learning system is used, composed
of a Universal Grammar with associated parameters, and a learning algorithm,
following the Principles and Parameters Theory. The Universal Grammar is
implemented as a Unification-Based Generalised Categorial Grammar, embedded
in a default inheritance network of lexical types. The learning algorithm receives
input from a corpus of spontaneous child-directed transcribed speech annotated
with logical forms and sets the parameters based on this input. This framework
is used as a basis to investigate several aspects of language acquisition. In this
thesis I concentrate on the acquisition of subcategorisation frames and word order
information, from data. The data to which the learner is exposed can be noisy and
ambiguous, and I investigate how these factors affect the learning process. The
results obtained show a robust learner converging towards the target grammar
given the input data available. They also show how the amount of noise present
in the input data affects the speed of convergence of the learner towards the
target grammar. Future work is suggested for investigating the developmental
stages of language acquisition as predicted by the learning model, with a thorough
comparison with the developmental stages of a child. This is primarily a cognitive
computational model of language learning that can be used to investigate and
gain a better understanding of human language acquisition, and can potentially
be relevant to the development of more adaptive NLP technology.
4
Acknowledgements
First of all, I want to express my gratitude to my supervisor, Ted Briscoe, for
all his support, for making this whole project more enjoyable with his excellent
discussions, and for his patience during stressful times. I’m grateful to Ann
Copestake for her friendly support, and for innumerable suggestions and solutions
to the most varied problems. Many thanks to Karen Sparck Jones and Stephen
Pulman for broadening my knowledge of natural language processing. I’m also
indebted to Ben Waldron for allowing me to use his system. I also want to thank
all the people that at one stage or another contributed to this work, especially
Julia Hockenmaier, Judita Preiss, Claire Taylor and James Thomas for their
comments on the thesis.
Thanks to all the staff at the Computer Laboratory who were always so
friendly, and made my life easier during the PhD. I am also grateful for the generous travel grants given to me by both the Computer Laboratory and Hughes
Hall. The research reported on this thesis was supported by a doctoral studentship from CAPES/Brazil. Thanks to everyone from CAPES, especially to
Vanda Lucena.
My time in Cambridge was made happier with the presence of all the friends
that I made here, among them: Martin Choquette, Pierre Jourlin, Sylvia Knight,
Olivia Kwong, Naila Mimouni, Miles Osborne and Donnla NicGearailt, Tetsuya
Sakai, Advaith Siddharthan, Jana Sukkarieh and James Thomas. Anna Korhonen
was a constant source of friendship, since we started the MPhil and throughout
our PhDs. To all the many friends that entered my life during this period, thank
you all for your friendship and encouragement.
All the support I received from my family in Brazil was a constant motivation
for completing the PhD. Ricardo, Ingrid, Hilda, Fabio, Ricardo Neto and Bianca
with their love and wisdom made me see how beautiful life can be. Finally, I’d
like to thank my husband Fabio Nemetz, without whose love, support, patience
and friendship, this research would never have been finished, and to whom this
thesis is dedicated.
5
6
Contents
1 Introduction
1.1 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . . . .
18
20
2 Literature Review
2.1 Universal Grammar . . . . . . . . . .
2.1.1 Triggers . . . . . . . . . . . .
2.1.2 Negative evidence . . . . . . .
2.2 Learners . . . . . . . . . . . . . . . .
2.2.1 Categorial Grammar Learning
2.2.2 Parameter Setting Learning .
2.3 Learning Paradigms . . . . . . . . . .
2.3.1 Identification in the Limit . .
2.3.2 PAC-Learning . . . . . . . . .
2.3.3 Minimum Description Length
2.4 Summary . . . . . . . . . . . . . . .
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23
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3 Grammar Encoding
3.1 Inheritance Hierarchies . . . .
3.2 Types . . . . . . . . . . . . . .
3.3 Defaults . . . . . . . . . . . . .
3.4 Lexical Rules . . . . . . . . . .
3.5 Asymmetric Default Unification
3.6 Symmetric Default Unification .
3.7 Summary . . . . . . . . . . . .
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40
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54
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67
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4 Unification-Based Generalised CG
4.1 Categorial Grammars . . . . . . . .
4.1.1 AB-Categorial Grammar . .
4.1.2 Extensions to AB-Categorial
4.2 UB-GCGs . . . . . . . . . . . . . .
4.2.1 Syntax . . . . . . . . . . . .
4.2.2 Semantics . . . . . . . . . .
4.2.3 Linking . . . . . . . . . . .
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Grammar
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4.3
4.4
4.5
4.6
4.7
4.2.4 The Grammar . . . . . . . . . . .
Rules . . . . . . . . . . . . . . . . . . . .
4.3.1 Morphological and Lexical Rules
4.3.2 Grammatical Rules . . . . . . . .
Coverage . . . . . . . . . . . . . . . . . .
4.4.1 Verbal Constructions . . . . . . .
4.4.2 Unbounded Dependencies . . . .
4.4.3 Coordination . . . . . . . . . . .
A Possible Universal Grammar . . . . .
The Annotated Sachs Corpus . . . . . .
Summary . . . . . . . . . . . . . . . . .
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5 Learning a Lexicon
5.1 Learning the Meanings of Words . . . . . . .
5.1.1 The Algorithm . . . . . . . . . . . .
5.1.2 Evaluation of the Semantics Learner
5.2 Learning the Syntactic Category of Words .
5.2.1 The Algorithm . . . . . . . . . . . .
5.2.2 Evaluation of the Syntax Learner . .
5.3 Summary . . . . . . . . . . . . . . . . . . .
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6 The Learning System
6.1 Architecture of the Learning System . . . . .
6.2 Bayesian Incremental Parameter Setting . . .
6.2.1 The Implemented Learning Algorithm
6.3 Summary . . . . . . . . . . . . . . . . . . . .
7 The Learning Tasks
7.1 Learning Categories . . . . . . . . . . . .
7.2 Learning from Ambiguous Triggers . . .
7.2.1 Argument or Adjunct? . . . . . .
7.3 Learning Word Order Parameters . . . .
7.3.1 The Unset Learner: a Basic Case
7.3.2 Different Starting Points . . . . .
7.3.3 Learning in a Noisy Environment
7.4 Summary . . . . . . . . . . . . . . . . .
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76
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170
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8 Conclusions and Future Work
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8.1 Results and Achievements . . . . . . . . . . . . . . . . . . . . . . 206
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Bibliography
212
8
9
List of Acronyms and
Abbreviations
AB-CG
AVS
BIPS
CCG
CG
CUG
FS
HPSG
MDL
MLE
NLP
N
NP
PAC-learning
PP
PRT
PPT
OVS
RNR
S
SCG
SOV
STL
SVO
TDFS
AB-Categorial Grammar
Attribute-Value Specification
Bayesian Incremental Parameter Setting
Combinatory Categorial Grammar
Categorial Grammar
Categorial Unification Grammar
Feature Structure
Head-Driven Phrase Structure Grammar
Minimum Description Length
Maximum Likelihood Estimation
Natural Language Processing
Noun
Noun Phrase
Probably Approximately Correct Learning
Prepositional Phrase
Particle
Principles and Parameters Theory
Object-Verb-Subject
Right Node Raising
Sentence
Stochastic Categorial Grammar
Subject-Object-Verb
Structural Triggers Learner
Subject-Verb-Object
Typed Default Feature Structure
10
TFS
Typed Feature Structure
TLA
Triggering Learning Algorithm
UB-GCG Unification-Based Generalised Categorial Grammar
UCG
Unification Categorial Grammar
UG
Universal Grammar
VCA
Valid Category Assignment
VSO
Verb-Subject-Object
11
List of Figures
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
Pollard and Sag’s Hierarchy . . . . . . . . . . . . . . . . . . . .
Fragment of a Type Hierarchy . . . . . . . . . . . . . . . . . . .
Specification of a Complex Feature Structure . . . . . . . . . . .
Specification of Another Complex Feature Structure . . . . . . .
Constraint on Type modal . . . . . . . . . . . . . . . . . . . .
Lexical Description for could . . . . . . . . . . . . . . . . . . . .
Expanded Feature Structure for could . . . . . . . . . . . . . .
Lexical Description for ought . . . . . . . . . . . . . . . . . . .
Expanded Feature Structure for ought . . . . . . . . . . . . . .
HPSG Third Singular Verb Formation Lexical Rule . . . . . . .
Abbreviated Form of the Lexical Rule . . . . . . . . . . . . . . .
Reinterpreted Third Singular Verb Formation Lexical Rule . . .
Lexical Description for the Base Form of love . . . . . . . . . .
Asymmetric Default Unification of Output and Input Structures
Application of the Third Singular Verb Formation Lexical Rule .
Skeptical Asymmetric Default Unification . . . . . . . . . . . . .
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4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
Using Forward Application . . . . . . . . . . . . . . . . . . . . . .
First Derivation of Sentence John likes Mary . . . . . . . . . . . .
Second Derivation of Sentence John likes Mary . . . . . . . . . .
Using Forward Composition . . . . . . . . . . . . . . . . . . . . .
Using Forward Type Raising . . . . . . . . . . . . . . . . . . . . .
Using Backward Type Raising and Backward Composition . . . .
First Derivation of Sentence Bill runs here . . . . . . . . . . . . .
Second Derivation of Sentence Bill runs here . . . . . . . . . . . .
Derivation of Sentence She donated to the school those computers
Derivation of Sentence She donated those computers to the school
First Derivation of Sentence Jane eats the cake . . . . . . . . . . .
Second Derivation of Sentence Jane eats the cake . . . . . . . . .
Derivation of Sentence He gave Bill a guitar and Helen a piano .
UCG’s Encoding of walks . . . . . . . . . . . . . . . . . . . . . .
CUG’s Encoding of runs . . . . . . . . . . . . . . . . . . . . . . .
Sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Type Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . .
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12
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
4.26
4.27
4.28
4.29
4.30
4.31
4.32
4.33
4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.48
4.49
4.50
4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.58
4.59
4.60
NP sign . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Complex Category Type . . . . . . . . . . . . . . . . . . .
Intransitive Verb Type . . . . . . . . . . . . . . . . . . . .
Intransitive Verb Type Abbreviated . . . . . . . . . . . . .
Transitive Verb Type . . . . . . . . . . . . . . . . . . . . .
Traditional Encoding for Intransitive Verbs . . . . . . . . .
Traditional Encoding for Transitive Verbs . . . . . . . . .
Transitive Verb Type Expanded . . . . . . . . . . . . . . .
Transitive Verb Type Expanded and DefFilled . . . . . . .
Semantic Type . . . . . . . . . . . . . . . . . . . . . . . .
Sample Predication in restr . . . . . . . . . . . . . . . .
Equivalent Sample Predication restr . . . . . . . . . . .
Logical Form of the sentence Bill loves Mary . . . . . . . .
Lexical Description of love . . . . . . . . . . . . . . . . . .
The Linking Principle . . . . . . . . . . . . . . . . . . . .
Linking Principle Applied to love - HPSG Formulation . .
Linking Principle Applied to love - UB-GCG Formulation .
Basic Category . . . . . . . . . . . . . . . . . . . . . . . .
S Category . . . . . . . . . . . . . . . . . . . . . . . . . . .
NP Category . . . . . . . . . . . . . . . . . . . . . . . . .
PRT Category . . . . . . . . . . . . . . . . . . . . . . . . .
The Proposed Hierarchy . . . . . . . . . . . . . . . . . . .
Intransitive Verb Type . . . . . . . . . . . . . . . . . . . .
Transitive Verb Type . . . . . . . . . . . . . . . . . . . . .
Transitive Equi Verb Type Partially Expanded . . . . . . .
Subject-Control Verb Type . . . . . . . . . . . . . . . . . .
Transitive Verb Type Expanded and DefFilled . . . . . . .
Super-Equi Verb Type . . . . . . . . . . . . . . . . . . . .
Pollard and Sag’s Hierarchy . . . . . . . . . . . . . . . . .
Semantic Type . . . . . . . . . . . . . . . . . . . . . . . .
Fragment of the Verbal Semantic Hierarchy . . . . . . . . .
One-arg-verb Semantics . . . . . . . . . . . . . . . . . . .
Two-arg-verb Semantics . . . . . . . . . . . . . . . . . . .
Fragment of the Verbal Linking Hierarchy . . . . . . . . .
One-arg-verb-linking Type . . . . . . . . . . . . . . . . . .
Intrans-raising-linking Type . . . . . . . . . . . . . . . . .
Two-arg-verb-linking Type . . . . . . . . . . . . . . . . . .
Three-arg-verb-linking Type . . . . . . . . . . . . . . . . .
Intrans-sign Type Expanded and DefFill ed . . . . . . . . .
Fragment of the Verbal Sign Hierarchy . . . . . . . . . . .
Plural Noun Morphological Rule . . . . . . . . . . . . . . .
dog Sign . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plural Noun Morphological Rule Applied to dog . . . . . .
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68
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4.61 Third Singular Verb Morphological Rule . . . . . . . . . . . . .
4.62 Non Third Singular Verb Morphological Rule . . . . . . . . . . .
4.63 Past Participle Verb Morphological Rule . . . . . . . . . . . . .
4.64 Inverted Modal Rule . . . . . . . . . . . . . . . . . . . . . . . .
4.65 Imperative Rule . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.66 Dative Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.67 Passive Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.68 Passive without Oblique Argument Rule . . . . . . . . . . . . .
4.69 Forward Application . . . . . . . . . . . . . . . . . . . . . . . .
4.70 Backward Application . . . . . . . . . . . . . . . . . . . . . . .
4.71 Forward Composition . . . . . . . . . . . . . . . . . . . . . . . .
4.72 Generalised Weak Permutation . . . . . . . . . . . . . . . . . .
4.73 Derivation of Sentence He bought fish and cooked dinner . . . .
4.74 Derivation of Sentence Bob backed the team up . . . . . . . . . .
4.75 Derivation of Sentence Bob backed up the team . . . . . . . . . .
4.76 Sentence Bill runs . . . . . . . . . . . . . . . . . . . . . . . . .
4.77 Derivation for a Transitive Construction . . . . . . . . . . . . .
4.78 Derivation of Sentence Bill gave Mary the dog . . . . . . . . . .
4.79 Derivation of Sentence Bill tries to run . . . . . . . . . . . . . .
4.80 Logical Form of Sentence Bill tries to run . . . . . . . . . . . .
4.81 Derivation of Sentence Bill tends to run . . . . . . . . . . . . .
4.82 Logical Form of Sentence Bill tends to run . . . . . . . . . . . .
4.83 Derivation of Sentence Goldie warms up the milk . . . . . . . .
4.84 Derivation of Sentence Goldie warms the milk up . . . . . . . .
4.85 Abbreviated Lexical Entry for warm, with pform:up . . . . . .
4.86 Derivation of Sentence He put the book on the shelf . . . . . . .
4.87 Derivation of Sentence Give me that pillow . . . . . . . . . . . .
4.88 Derivation of Sentence This watch was bought by Mary . . . . .
4.89 Derivation of Sentence Mary bought this watch . . . . . . . . . .
4.90 Sign for the Auxiliary have . . . . . . . . . . . . . . . . . . . . .
4.91 Derivation of Sentence Will Mary buy the car? . . . . . . . . . .
4.92 Derivation of Sentence Who does love Bill? . . . . . . . . . . . .
4.93 Derivation of Sentence Where did John put the keys . . . . . . .
4.94 Derivation of Sentence Where does John live? . . . . . . . . . .
4.95 Derivation of Sentence The person who loves Bill hates Bob . . .
4.96 Derivation of Sentence The house where John lives has a garden
4.97 Derivation of Sentence My brother and sister gave me a book . .
4.98 Derivation of Sentence I like John and Mary . . . . . . . . . . .
4.99 Derivation of Sentence Kim brought a pizza and John ate a slice
4.100Derivation of Sentence You read and I taped the story . . . . . .
4.101Derivation of Sentence The man cooked and ate potatoes . . . .
4.102Derivation of Sentence She smiled and gave him a gift . . . . . .
4.103Derivation of Sentence Jane gave Bob a dog and Sue a cat . . .
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111
4.104Fragment of the Categorial Parameters Hierarchy . . . . . . . . . 112
4.105Specification of intrans-par Type . . . . . . . . . . . . . . . . . . 113
4.106Specification of intrans-sign Type . . . . . . . . . . . . . . . . . . 113
4.107Fragment of the Parameters Hierarchy . . . . . . . . . . . . . . . 115
4.108Gendir Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.109Subjdir Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.110Vargdir Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.111Subjdir Parameter Expanded . . . . . . . . . . . . . . . . . . . . 117
4.112Subjdir Parameter after Trigger . . . . . . . . . . . . . . . . . . . 117
4.113Interaction of the Transitive Verb Type with the Vargdir Parameter117
4.114Transitive Verb Type Expanded . . . . . . . . . . . . . . . . . . . 117
4.115SOV to SVO Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.116Sentence I will take him . . . . . . . . . . . . . . . . . . . . . . . 121
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
Architecture of the Learning System . .
Word Order Parameters - Hierarchy 1 . .
Word Order Parameters - Hierarchy 2 . .
Word Order Parameters - Hierarchy 3 . .
Possible Hierarchy 1 . . . . . . . . . . .
Possible Hierarchy 2 . . . . . . . . . . .
Possible Hierarchy 3 . . . . . . . . . . .
Transitive Verb Type Partially Expanded
Specification of Intransitive Verb Type .
Specification of Transitive Verb Type . .
Fragment of the Parameters Hierarchy .
Word Order Parameter - Hierarchy 4 . .
Word Order Parameter - Hierarchy 5 . .
Word Order Parameter - Hierarchy 6 . .
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7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
Intransitive Verb Type Partially Expanded . . .
Transitive Verb Type Partially Expanded . . . .
Current Hierarchy . . . . . . . . . . . . . . . . .
Insertion Place for the Transitive Verb Type - 1
Insertion Place for the Transitive Verb Type - 2
Insertion Place for the Transitive Verb Type - 3
Specification of Transitive Verb Type . . . . . .
Transitive Verb Type - Alternative 1 . . . . . .
Transitive Verb Type - Alternative 2 . . . . . .
Possible Linking Pattern - 1 . . . . . . . . . . .
Possible Linking Pattern - 2 . . . . . . . . . . .
Possible Linking Pattern - 3 . . . . . . . . . . .
Possible Linking Pattern - 4 . . . . . . . . . . .
Possible Linking Pattern - 5 . . . . . . . . . . .
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7.15
7.16
7.17
7.18
7.19
7.20
7.21
7.22
7.23
7.24
7.25
7.26
7.27
7.28
7.29
7.30
Possible Linking Pattern - 6 . . . . . . . . . . . . . . . . . . .
Specification of Transitive Linking Pattern Expanded . . . . .
Specification of Oblique Transitive Linking Pattern . . . . . .
Fragment of Hierarchy of World Knowledge . . . . . . . . . .
Performance of the Unset Learner . . . . . . . . . . . . . . . .
Convergence of the Unset Learner . . . . . . . . . . . . . . . .
Learners-10 in a Normal Environment . . . . . . . . . . . . . .
Convergence of Subjdir - Learners-10 - Noisy Environment . .
Convergence of Subjdir - Learners-50 - Noisy Environment . .
Learners’ Performances in a Noisy Environment . . . . . . . .
Learners’ Performances in Different Environments . . . . . . .
Convergence of Subjdir - Learners-10 - Noise-free Environment
Convergence of Subjdir - Learners-50 - Noise-free Environment
Learners’ Performances in all the Different Environments . . .
Learner’s Performance with Different Levels of Noise . . . . .
Convergence of Subjdir with Different Levels of Noise . . . . .
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203
204
List of Tables
4.1
4.2
4.3
Categorial Parameters . . . . . . . . . . . . . . . . . . . . . . . . 113
Types and Parameters . . . . . . . . . . . . . . . . . . . . . . . . 115
Ten Most Frequent Open-Class Words . . . . . . . . . . . . . . . 122
6.1
6.2
Initialisation of a Parameter . . . . . . . . . . . . . . . . . . . . . 163
Status of a Parameter . . . . . . . . . . . . . . . . . . . . . . . . 164
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
Frequency Information about Locative PPs . . . . . . . .
Sentences with put without a Locative PP . . . . . . . .
Disambiguation of Locative PPs . . . . . . . . . . . . . .
Convergence of the Unset Learner . . . . . . . . . . . . .
Initialisations of the Different Learners . . . . . . . . . .
Initial Weights of the Different Learners . . . . . . . . .
Initialisations of the Different Learners-10 . . . . . . . .
Convergence of the Different Learners - Condition 1 . . .
Initialisations of the Different Learners-50 . . . . . . . .
Convergence of the Different Learners - Condition 2 . . .
Convergence of the Different Learners - Condition 3 . . .
Convergence of the Different Learners - Condition 4 . . .
Convergence of the Learner with Different Levels of Noise
17
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185
185
187
189
192
193
193
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201
203
Chapter 1
Introduction
Over the last four decades, researchers in the Natural Language Processing (NLP)
community have been developing techniques to enable computers to understand
human language. Traditionally, NLP systems use manually constructed resources
containing linguistic information. The construction of these resources is labour
intensive and time consuming, and results in static and inflexible resources.
Due to the open-ended and constantly evolving nature of natural languages,
researchers have started to investigate how to equip natural language processing
systems with learning models for automatically acquiring linguistic information.
Such systems would have the capacity to constantly evolve with their linguistic
environments. In this way, a system would be prepared to handle novel uses
of linguistic constructions, which can be introduced in a given language, for instance, by communities of speakers, either in the more traditional sense of regional
communities, but also communities such as mobile phone users, computer users,
business people, and so on. Moreover, such systems should be robust to noise in
the linguistic environment. The need for systems that can dynamically adapt to
their linguistic environment has increased with the necessity of processing huge
quantities of unrestricted data that are currently available, thanks to advances
in technology.
In trying to solve the question of how to get a machine to automatically learn
linguistic information from data, we can look at the way people do it. The acquisition of language from data is a task that we humans do when we acquire
our mother language. Children acquire a grammar that corresponds to their
language just by being exposed to a linguistic environment. This environment
includes noisy and ungrammatical sentences, the potential influence of other languages, and many other linguistic phenomena. In spite of that, most children are
successful in the acquisition of a grammar in a relatively short time, acquiring a
sophisticated mechanism for expressing their ideas, based on data that is noisy
and said to be too impoverished to generate such a complex capacity. One approach to explain the acquisition of languages proposes that children must have
some innate knowledge about language, a Universal Grammar (UG), to help them
18
overcome the problem of the poverty of the stimulus and acquire a grammar on
the basis of positive evidence only [Chomsky 1965]. According to Chomsky’s
Principles and Parameters Theory [Chomsky 1981], the UG is composed of principles and parameters, and the process of learning a language is regarded as the
setting of values of a number of parameters, given exposure to this particular
language.
These ideas about human language acquisition are employed, in this work,
in the construction of a computational learning system that can learn from its
linguistic environment, which may contain noise and ambiguities. Studies like
this can also be used to help us understand better the process of human language
learning, but if that is to be achieved, we need to concentrate only on algorithms
and resources that a human learner could employ. Thus, there are significant
constraints on the assumptions that can be made in the learning system implemented. In this way, the learner cannot have access to negative information,
which is a source of information used by a number of learning algorithms. The
learner also cannot start with information specific to a particular language, and
can only assume information that is general among human languages. Another
aspect is that learning has to be on-line and incremental, with the system only
processing one sentence at a time, without the possibility of storing sentences
and reprocessing previously seen sentences, or doing multiple passes through the
corpus. Moreover, the kind of data given to the learner must be compatible with
the linguistic environment of a child. In this work the linguistic environment of
the learner is recreated using spontaneous child-directed speech in English, which
was phonemically transcribed, taken from the Sachs corpus [MacWhinney 1995]
and [Sachs 1983]. Children can use semantic and contextual information when
processing sentences, and semantic information is introduced in the corpus by
annotating the sentences with logical forms. In many psychological studies children were observed to be sensitive to statistical patterns in the data to which
they are exposed; in this work the learning system is also sensitive to statistical
patterns occurring in the input data.
The wider goal of this project is to investigate the process of grammatical
acquisition, and the focus of this work is on particular aspects, namely the acquisition of subcategorisation frames and word order information from data, and
the effect of noise and ambiguity in the learning process. This work involved
building a learning system, determining an appropriate form for the UG with
principles and parameters, studying the relations between the parameters and
the data that sets each of them, and implementing an appropriate learning algorithm. The UG is represented as a Unification-Based Generalised Categorial
Grammar (UB-GCG), and is embedded in a default inheritance hierarchy. The
UG provides the core knowledge about grammars that the learner has, and a
learning algorithm fixes the parameters to a particular language based on exposure to it. Moreover, a UB-GCG for English is implemented, and this grammar is
used to annotate the parents’ sentences from the Sachs corpus with the appropri19
ate logical forms. This corpus, which we refer to as the annotated Sachs corpus,
is then given as input to the implemented learning system, and it simulates some
of the environment in which a child acquires her language.
The learning environment contains noise and ambiguity and the learner has to
be able to deal with these problems if it is to converge to the target. In this
work the ambiguity is in the form of locative Prepositional Phrases that can
occur either as arguments to a verb or as adjuncts, and the noise is caused by
sentences where the thematic roles in the associated logical form are incorrectly
specified, corresponding to the cases where the learner is uncertain about the
thematic roles. Faced with the input data provided by the annotated Sachs
corpus, the learner has to set the parameters of the UG accordingly to be able
to successfully process this data. The learning algorithm implements a Bayesian
Incremental Parameter Setting (BIPS) learner [Briscoe 1999], and when setting
the parameters it uses a Minimum Description Length (MDL) style bias to choose
the most probable grammar that describes the data well. Several experiments are
conducted for testing the performance of the learner in different environments,
and the results obtained are analysed to determine the success of the learner in
the language learning tasks. In this evaluation, the English UB-GCG serves as
the target grammar, to which the learner has to converge in the learning tasks.
1.1
Structure of the Thesis
This thesis is organised into eight chapters, where chapters 2 and 3 provide some
background concepts that are important for the investigation conducted in the
thesis. Chapter 2 provides an overview of the relevant research in Linguistics and
Psychology about human language acquisition, and in Computer Science about
language learning systems.
Chapter 3 presents a discussion of the methods and techniques for encoding
grammatical knowledge that have been successfully employed in natural language
processing. Given that we are interested in efficient ways of representing linguistic
information, this discussion provides the necessary background from Linguistics
and NLP for this topic.
This is followed, in chapter 4, by a description of the Unification-Based Generalised Categorial Grammar implemented for English as part of this thesis. This
English UB-GCG implements several ideas and insights from linguistics and computational linguistics, and represents them using defaults. In this way, the grammar joins together many proposals about the use of defaults, and also implements
new ideas for the application of defaults proposed in the scope of this thesis. This
chapter also proposes a model of the UG in terms of UB-GCGs. The UG and
its principles and parameters are embedded in a default inheritance hierarchy,
which is a structure that is likely to be used in human processing for representing
and classifying several types of concepts. A description of the different types of
20
parameters defined is provided. Finally, chapter 4 also contains a description
of the annotated Sachs corpus, discussing the annotation undertaken and the
characteristics of the constructions found in the corpus.
In chapter 5 we describe two systems developed by Waldron [1999] that are
used to pre-process each sentence as it is given as input to the learning system.
These systems assign candidate logical forms and syntactic categories to the words
in a sentence. We present a detailed description of each of the systems, as well
as an evaluation of their performance in relation to the annotated Sachs corpus.
As discussed in the evaluation, these systems are prone to errors, being able to
correctly assign semantic and syntactic categories to only a small portion of the
corpus.
This is followed by a description, in chapter 6, of the learning system developed. The learning system implements a Bayesian Incremental Parameter Setting
algorithm [Briscoe 1999], which uses an MDL-style bias to set the parameters of
the grammar. The original algorithm proposed by Briscoe is adapted for learning
within a unification-based framework. The learning system needs to be able to
learn new and more complex categories, and include them in the currently used
grammar. It also needs to set the parameters according to the linguistic input
it receives. During the learning task, the learner collects statistical information
about the data and uses this information to help in obtaining the most concise
encoding for the grammar, according to the MDL-style bias.
Chapter 7 describes the learning tasks that the learner has to perform for
setting its parameters according to the language of the environment. Initially,
the learner starts with a small set of categories that can be used to process the
sentences, and, as learning progresses, more complex categories are also learned.
During the learning process, some of the sentences that the learner receives are
ambiguous, and the learner has to solve this ambiguity before learning can proceed. We concentrate on investigating the ambiguity caused by locative Prepositional Phrases, which can occur as arguments of the verb or as adjuncts. Once
the ambiguity is solved, the learner can proceed as usual and set the parameters
of the UG. Moreover, there are several possible starting points for the learner in
the learning tasks: the learner can start with its parameters unset, but it can
also have some parameters that are initially set to certain values, as defaults.
This is an important point, which in some learning systems described in the literature ([Gibson and Wexler 1994], [Berwick and Niyogi 1996] and [Kohl 1999])
was shown to determine whether the learner would converge to the target or not.
Since the starting point can affect the performance of the learner, we investigate
several possible starting points and analyse the different results obtained. Furthermore, during the learning process, some sentences may contain noise, and this
noise interferes with the convergence of the learner to the target grammar. We
investigate how the learner performs when facing different levels of noise provided
by different environments.
Finally, we present some conclusions, with an analysis of the contributions of
21
this work:
• the integration of several ideas on the use of defaults in linguistic description,
• the proposal of a plausible model of the Universal Grammar based on typological and linguistic studies, implemented as a UB-GCG, which allows
featural variation, being suited to capture natural languages,
• the development of a model of the UG embedded in a default inheritance
network of types that reduces of the amount of information that needs to
be learned because the information is passed by default from supertypes to
subtypes, so that even if a parameter has not been set, it already has the
inherited value,
• the development of a computational system where learning is based on
principles such as the Categorial Principles developed for independent reasons, and that uses the default inheritance network and the MDL Principle
for learning. Such a system can successfully learn from a corpus of real
child-directed data, containing noise and ambiguity, in a computational account of parameter setting that is compatible with several characteristics
of human language acquisition.
We conclude with a discussion of future work that can be developed given the
framework implemented in this research.
22
Chapter 2
Literature Review
In this work we are interested in investigating the learning of grammatical knowledge from data. A learning situation usually involves five elements [from Bertolo
2001]:
• the concept being learned,
• the kind of hypotheses that the learner can formulate,
• the environment providing the data to the learner and defining the order
of presentation of this data,
• the learning framework which defines the restrictions for the updating of
the hypotheses in relation to the presentation of data, and
• the conditions for success of the learner.
A learner can be seen as an individual equipped with a learning procedure
which can map a set of input examples into hypotheses that can classify the
examples. The concept being learned in the scope of this study is a language
from the set of natural languages.
The hypotheses in relation to the target concept are expressed by means
of grammars that can classify the input examples as generated or not by the
grammar of the target language. In this work, the grammar space is composed of
grammars that are allowed by a model of a Universal Grammar [Chomsky 1965],
defined in terms of principles and parameters. Following the Principles and Parameters Theory (PPT), the parameters of the UG are set to a particular grammar that provides the linguistic environment to which the learner is exposed, as
is described in section 2.1.
The environment provides the data given to the learner, which consists of
sentences produced by the target language. Besides providing the examples, a
learning environment can also correctly inform whether a given example is in
the target or not, it can incorrectly inform, or it can remain silent. Certain
23
environments can provide infinitely many examples to the learner while others
can provide only a finite number of examples. Some environments may present
the examples according to a certain rule known to the learner, and this makes
the learning task easier. One widely investigated notion of environment is that
of a text that is defined by Gold [1967] as an infinite sequence of sentences for a
given language L such that every sentence of L appears at least once in it and
no sentence that is not in L appears in it. As far as this work is concerned, the
environment is a finite subset of a text that provides sentences annotated with
logical forms, extracted from a corpus of parents’ sentences to a child, which
presents the sentences in the order in which they were produced.
Learners can follow different strategies. For instance, some use past evidence
to decide on which hypothesis to select next, having a perfect memory. Others
are memory-less and do not use any past data to choose their next hypothesis,
possibly revisiting past hypotheses. There are also those that only modify their
current hypothesis when it is incompatible with the current example, among other
possible learners. This is discussed in section 2.2.
The last element is a criterion of success, which is used to evaluate whether
a learning strategy is successful or not. Two widely used learning paradigms are
Identification in the Limit and Probably Approximately Correct (PAC) learning.
These two paradigms are considered to be too strict to be used in practical situations [Bertolo 2001]. Nonetheless, as demonstrated in [Bertolo 2001], if a class
of languages is generated by a class of grammars consistent with the Principles
and Parameters Theory, it is learnable under each of the criteria. An alternative
to the first two paradigms is the Minimum Description Length Principle (MDL)
that is an algorithmic paradigm for defining learners, which has been successfully
used in several computational learning systems. These learning paradigms are
discussed in section 2.3.
2.1
Universal Grammar
One of the remarkable facts about languages is that, although they are complex
systems, children learn them reliably and in a short period of time. As Hyams
[1986] observes, children have to learn the form and meaning of individual lexical
items used in their languages; they must develop a processing system to generate
and comprehend sentences; they must learn pragmatic and social skills to be
able to use language appropriately in different contexts; and they must learn
the grammar that corresponds to their language. However, the data to which
children are exposed is so limited that it cannot provide an explanation of how it
is that children achieve all the aspects of the mature state [Lightfoot 1991]. This
problem, known as the poverty of the stimulus, arises because, in general, the
learner is exposed to simple grammatical input, which for the most part consists
of sentences without much embedding, and, as observed by Gleitman and Wanner
24
[1982], that are “propositionally simple, limited in vocabulary, slowly and carefully
enunciated, repetitive, deictic, and usually referring to the here and now ”. So how
can children based on this data arrive at a mature state that is so sophisticated?
According to Lightfoot [1991], the input to which children are exposed is poor in
three ways [from Lightfoot 1991, p. 3]:
• “The child’s experience is finite, but the capacity eventually attained ranges
over an infinite domain, and therefore must incorporate some recursive
property not demanded by experience”. Children do not simply imitate what
they hear, or memorise the list of all sentences to which they are exposed,
but they create new sentences, which suggests that they have an internal
system of rules that allows them to creatively produce new sentences.
• “The experience consists partly of degenerate data which have no effect on
the emerging capacity”. The linguistic environments to which children are
exposed may contain noise and interruptions, may be influenced by another
language, and so on. Nevertheless, children successfully converge to their
target language.
• “Most importantly, it fails to provide the data needed to induce many principles and generalisations manifested by the mature capacity”. For instance,
the relation between a declarative sentence such as The book on the shelf
is expensive, and a question such as Is the book on the shelf expensive? is
learned, even though this is not explicitly stated when each of these examples is presented to the learner. Moreover, such a relation can be applied to
other sentences, not being exclusive to the particular words used in these
two sentences, which suggests that the learner must be making generalisations from specific examples.
A child has to learn a language just by being exposed to it and without, in
general, receiving any feedback about possible errors it makes. Furthermore, the
linguistic environments to which children are exposed have a variety of different
dialects and possibly more than one language. However, children are robust to
this variety of influences and successfully learn the languages and dialects to
which they are consistently exposed. The question that arises is: ‘How does this
work?’.
Chomsky’s proposed explanation [Chomsky 1965] is that humans must have
some innate knowledge about languages, and, as a consequence, they do not need
to learn some of the complex aspects of languages. Thus the hypothesis is that
children must have some innate knowledge about language that guides them and
helps them overcome the poverty of the stimulus, to acquire a grammar based
only on positive evidence and in a finite amount of time.
According to Chomsky’s [1981] Principles and Parameters Theory, this core
common knowledge, or Universal Grammar, is composed of a set of principles and parameters. The principles constitute the child’s prior knowledge of
25
languages, representing characteristics that are common across languages. The
parameters represent the points of variation across them and are fixed to a particular language based on exposure to a given linguistic environment. This theory
suggests that human languages follow a common set of principles and differ among
one another only in finitely many respects, represented by the parameters. As
there is a finite number of parameters, that can take a finite number of values,
there is a finite number of languages that the learner needs to consider, instead
of an infinite space of possibilities. This constrains the class of languages that
can be learned and makes language acquisition possible in principle. By setting
the parameters of the UG to the appropriate values, based on exposure to a particular linguistic environment, the result is the selection of the grammar that can
account for the input sentences, among all the various possible grammars allowed
by the UG. The sentences that activate the setting of the parameters are called
triggers, as discussed in section 2.1.1.
The form of the UG is still an unresolved question. While it has to be restrictive enough to allow language acquisition to happen on the basis of poor stimulus
in a finite amount of time, it has to be general enough to allow for the range of
possible human languages.1
One possible source of additional information consists of the statistical properties of the data to which children are exposed. This data presents statistical
properties that can potentially be used during the learning process. It may be
the case that children ignore this source of information, but if they do use it,
it could help them minimise several of the difficulties that they face. Moreover,
noise resistance may be explained in terms of sensitivity to statistical properties
of the environment. As Clark [2001] observed, recent work in psycholinguistics
has indicated that children are indeed sensitive to these statistical properties
([Redington and Chater 1998] and [MacDonald 1999]).2 Furthermore, children
may also gather additional information from the context in which they hear sentences. As Pinker [1995] remarked, children do not hear sentences in isolation but
in a context. Thus, when a child interacts with other speakers, these tend to talk
more about the here and now, and the child can observe the context and guess
what the speaker might have meant. In fact, many models of language acquisition
assume that the input the child receives consists not only of the sentence, but also
of a representation of the meaning of the sentence ([Wexler and Culicover 1980],
[Pinker 1984], [Berwick 1985], [Briscoe 1999], among others). How much of the
context surrounding the hearing of a sentence is used by children is an open
question. Besides, as Landau and Gleitman [1985] observe, blind children have
a severely limited access to non-linguistic aspects of the world, but they succeed
in learning languages without many problems. However, it is reasonable to as1
For a discussion of possible parametric systems see Hyams [1986], Clark [1992], Culicover
[1997], Briscoe [1997 to 2000], among others.
2
Some computational systems of language acquisition that use statistical information are
described in [Kapur and Clark 1996], [Briscoe 1999] and [Yang 1999].
26
sume that children can use their knowledge about the current situation and the
meaning of familiar words in a sentence to try to understand (at least part of)
the sentences they hear.
As a child is exposed to its linguistic environment, a learning procedure sets
the values of the parameters such that the resulting grammar is usually equivalent
to that of the environment. The process of acquiring the target grammar can be
understood through Chomsky’s model of a child searching through a restricted
hypothesis space of grammars in order to select the correct one [Chomsky 1965].
Constraints help the learner get closer to the target hypothesis by excluding many
incorrect hypotheses that do not conform to these constraints [Berwick 1985].
The UG can then be considered a restriction in the hypothesis space, such that
it only contains those grammars that conform to the principles and to the possible assignments of values of the parameters. In this way, a child does not need
to consider every possible grammar, but only the ones consistent with the UG.
However, even in this restricted hypothesis space, if we assume that parameters
are binary-valued3 and that there are between 20 and 30 independent parameters, these give rise to between 220 (1,048,576) and 230 (1,073,741,824) estimated
possible grammars. Consequently an efficient search needs to be conducted.
2.1.1
Triggers
As already stated, the observed simplicity of the input to children has several
implications for learning, such as increasing the need for some sort of innate
learning device which would help the learner overcome the poverty of the stimulus.
Another implication is that, if children learn a language based on this simplified
input, it must be the case that all the data needed for setting the parameters of
the UG to the target language must be present in this simple input. The process
of setting the syntactic parameters is known as triggering, and the input that
provides evidence for the learner to set its parameters is known as a trigger.
Triggering is a particular type of learning where languages are perceived as
differing in terms of parameter settings. This is an alternative to another type
of learning referred to as hypothesis formation, where grammars are regarded
as rule systems that considerably vary from one language to another. As Sakas
and Fodor [2001] observe, such a type of learning has a much heavier workload
and does not seem to be suited to model human language learning, which is a
uniform and gradual process. Parameter setting, on the other hand, seems to be
less costly and much more uniform.
Precise definitions of triggers are hard to find and variable, but a commonly
used concept is that of a sentence of the target language that the learner detects
and uses to set the values of parameters to the target. Lightfoot [1991] defines
triggers as consisting of set of utterances haphazardly appearing in a given context
3
Throughout the document, unless otherwise stated, parameters are binary-valued.
27
of a type that any child hears very frequently, and not including any kind of
negative evidence.
But which sentences are triggers, and what form do these sentences have?
Clark [1992] defines the concept of a fair text, where triggers must be expressed in
sentences that are simple. He formalises the notion of parameter expression,
where a sentence expresses a certain parameter if it requires the grammar to
have that parameter set to a particular value for the sentence to be grammatical.
Any input sentence can express parameters, and a sentence is a trigger for a
parameter if it expresses that parameter. Thus, for a system of parameters to
be learnable, there must exist triggers for all the values of its parameters in the
input data, and the learner must be able to detect them. Furthermore, Clark also
defines the notion of frequency of parameter expression, which states that
triggers for each of the parameters must occur above some minimal frequency
in the data. Then, given that the learner needs to be able to resolve possible
ambiguities, it must be the case that the target settings must be expressed with
a higher frequency than alternative non-target settings. Besides that, it must be
guaranteed that the parameters can be expressed in simple structures that are
likely to occur in the learner’s environment, and this guarantee is formalised as
the boundedness of parameter expression.
Some computational learning algorithms, like the Triggering Learning Algorithm (TLA) [Gibson and Wexler 1994], need triggers to activate them, and,
based on these sentences, they change the parameters of the UG to account for
a particular language. In an error-driven algorithm like the TLA, a trigger is
recognised by parsing failure, and it is used to signal a need for changing the
parameter settings. The learner then attempts to change the parameters in constrained ways, so that it can successfully parse the sentence.
The precise form of triggers is also varied. Are triggers expressed only in
the words in the sentences? Or are triggers also expressed in other sources of
information? For instance, Briscoe [Briscoe 1999] uses a notion of triggers that
consist of a sentence annotated with an appropriate logical form, from which
evidence for certain parameter values are obtained, making use of the meaning
of the sentence. Fodor’s Structural Triggers Learner (STL) [1998] uses treelets
obtained from input sentences as triggers. Treelets consist of subtrees containing
information about a derivation tree produced by a parser for a given sentence,
and they are used to set the parameters of the UG .
One important question regarding the use of triggers for parameter setting is
that it presupposes that the learner can identify the relevant triggers in the input
data for each of the parameters. However, how does the learner detect triggers
automatically and reliably from the input sentences? How does it know which
parameter and which value is being triggered? Dresher and Kaye [1990] propose
that the learner is innately provided with the knowledge of the cues (triggers)
associated with every parameter and, when the input provides cues, the learner
sets the values corresponding to the relevant parameters. Kapur and Clark [1994]
28
investigate the problem of trigger detection using some statistical properties of
the data. They define a learner that analyses the patterns in the occurrence of
certain phenomena and uses these patterns to set the parameters of the UG.
Thus, learners detect triggers in the data and use them to set the parameters of
the UG. But do all triggers provide reliable evidence for a particular value? Clark
[1992] discusses the problem of indeterminacy of parameter expression,
where a given trigger may be consistent with different parameter values. One such
case is that of word order ambiguity, where the surface order of constituents in an
input sentence may not reflect the underlying word order. For example, German,
whose canonical order is Subject-Object-Verb (SOV), also accepts Subject-VerbObject (SVO) orders due to the verb second (V2) phenomenon, which moves
the verb to the second position. In this way, when an SVO sentence occurs, it
might have been generated by an SVO language such as English, but it might
also have been produced by an SOV-V2 language like German. The problem for
the learner is that not all triggers are going to be giving evidence for only one
parameter value, and the learner has to decide how to proceed when faced with
ambiguous triggers. Sakas [2000] examines the problem of ambiguous triggers
in relation to Fodor’s Structural Trigger Learner, where the variant of the STL
employed only learns from triggers that are unambiguous. From the results he
obtained, assuming that sentences contain a fixed number of triggers, such a
learning strategy would need an unreasonable number of input sentences to set
the parameters of the UG to the target language, since it needs to wait for
completely unambiguous triggers. The results obtained by Sakas are specific to
the STL model, but they highlight the importance of more investigation into the
relation between triggers and learning models, since this may clarify whether a
given model can present a reasonable account of language acquisition.
2.1.2
Negative evidence
As Pinker [1994] notes, children seem to acquire their native languages using
only positive evidence, in the form of sentences of their languages. However, to
clarify this issue some researchers investigated the possibility of the availability
of negative evidence too. The availability of negative information changes considerably the nature of the language learning problem, avoiding several of the
difficulties that arise when only positive evidence is available. Furthermore, if
negative evidence were available to the learner, it would have to occur in a systematic manner in the environment, in the same way as positive evidence does.
Indeed, many of the learnability proofs rely on such evidence being systematically
available in the environment. Gold [1967], in his learnability study, showed that
when only positive evidence was available in the form of a text, not even the
class of regular languages is identifiable in the limit, whereas if negative evidence
is provided by an informant, the class of languages that can be identified in the
limit includes that of context sensitive languages. Thus, the possibility of both
29
positive and negative information available for learning alters considerably the
acquisition problem.
Parents’ correction is considered by many to be a source of negative evidence.
However, even though some parents do correct their children, it is not true of
all parents, and as such it is not available to all children. Consequently the
occasional correction of grammatical errors cannot be regarded as systematically
available. Furthermore, in certain cultures not even the occasional correction is
available to children, which suggests that the possibility that children rely on
negative information for learning is extremely remote [Marcus 1993]. Moreover
when there is parental correction available, as Ingram [1992] observes, it is mostly
concerned with semantic appropriateness and in the cases where it is related to
syntax, besides the fact that in some cases it is difficult to know what is wrong,
children seem to be oblivious to this kind of correction. Thus, it does not seem
that the occasional correction that occurs so infrequently and unsystematically
can be used by children as explicit negative evidence to help them acquire their
languages.
2.2
Learners
The focus of this thesis is the acquisition of grammatical knowledge, in terms of
Categorial Grammars (CGs), within the Principles and Parameters framework.
Thus, this section provides an overview of some of the work done on the computational learning of CGs and on learning within the Principles and Parameters
Theory.
2.2.1
Categorial Grammar Learning
A considerable body of work has been developed for CG learning. Given a set
of input sentences generated by a particular language, these grammar learning
systems define the learning task as the search for a grammar to recognise and/or
generate all grammatical sentences in that language. In these systems, the learner
is given sentences from the target language as input, along with negative evidence
in some cases, from which they need to learn a grammar. In what follows, we
describe some of these systems, noting that a proper discussion of CG is provided
in chapter 4.
In terms of learnability, the basic AB-Categorial Grammars (AB-CG)
[Ajdukiewicz 1935], [Bar Hillel 1953], which employ a small set of categories and
only the rules of functional application, have good learning algorithms from
positive examples, when these examples are structured. Buszkowski and Penn
([Buszkowski 1987], and [Buszkowski and Penn 1990]) investigate the so-called
“discovery-procedures” for AB-CGs, which are algorithms for learning CGs from
functor-argument structures, with a resulting lexicon being generated where the
30
words are assigned the corresponding categories. These functor-argument structures are derivation tree structures, where each branch is annotated not with
category labels, but instead with an indication of the functor daughter. Such
results can be obtained for some classes of AB-CGs, such as the class of Rigid
Grammars, where each word in the lexicon has exactly one possible category.
Kanazawa [1998] further investigates the algorithms developed by Buszkowski
and Penn, exploring not only learning from functor-argument structures, but
also learning from flat strings of words. Kanazawa also discusses how the learnability results obtained can be adapted to variants of CG, such as Combinatory
Categorial Grammars (CCG) [Steedman 1985 to 2000], which employ larger sets
of categories and/or rules than AB-CG.
Among the computational systems developed for learning CGs, we now look
at three systems: Adriaans’ EMILE [1992], Watkinson and Manandhar’s [2000]
unsupervised learning system, and Osborne and Briscoe’s [1997] Stochastic Categorial Grammar learner.
Adriaans ([Adriaans 1992] and [Adriaans and de Haas 2000]) defines EMILE
as a system that performs CG induction within the PAC-learning framework,
which is discussed in section 2.3.2. The learning algorithm has access to an oracle
that provides correct positive examples and also answers questions, providing
explicit negative evidence. Thus, the learner is allowed to ask questions about
the grammatical validity of new sentences. In the grammar learning task, the
learner assumes that each construction in the grammar can be exemplified by
means of a small and simple sentence. It also assumes that there is a higher
probability of the oracle using simpler sentences, and complex sentences have a
lower probability of occurring. Using the oracle, the system tests the hypothesis
generated about the categories in the grammar. Even though the system performs
well, it is in a highly supervised environment, receiving both positive and negative
input, so it is arguable whether it is a plausible approach to the study of human
language learning.
Watkinson and Manandhar [2000] developed a system for learning CGs from
unsupervised texts and without negative evidence. Their learner assumes that it
knows from the start the set of all the possible categories, and it is allowed to
start with a lexicon of closed class categories, such as prepositions and determiners. Then, for each word in a sentence the system tries to infer categories, from
the set of possible categories, which would provide successful derivations, using
the rules of functional application. During this process the system collects the
frequency of occurrence of each word with a particular category and stores this
in the lexicon too. The learner also maintains for each sentence processed, the
sentence and the N most likely parses. During learning, each time the lexicon is
modified, the system reparses the examples that were parsed before and that can
be affected by the changes in the lexicon, and it recomputes the frequencies of
the words, in case this reparsing finds new most likely parses. As a result of the
process, the system acquires a lexicon containing the categories assigned to the
31
words and their corresponding relative frequencies, induced from a corpus of raw
sentences. Furthermore, by storing the sentences with the N most likely parses
found, an annotation for these sentences is also obtained, and this can be used
as an annotated corpus. When the system is tested in an artificially generated
corpus, which contains 39 words and one case of verb-noun ambiguity, the system performs well, achieving 100% lexicon accuracy, in relation to the categories
assigned to the words, and 100% parsing accuracy. However, testing on a more
realistic corpus, which contains 554 sentences, was not as successful, achieving
73.2% lexicon accuracy and 28.5% parsing accuracy. The task attempted by
the system is very ambitious, and the system needs to rely on some sources of
information: the set of possible categories, the rules, and the closed class lexicon. However, it is arguable whether this system is a plausible model of human
language acquisition given its assumptions, especially about its access to all the
sentences previously parsed and the possibility of reparsing them when needed.
Osborne and Briscoe [1997] define a system that learns Stochastic Categorial
Grammar (SCG) from data, in a greedy, bottom-up, incremental manner. Initially, the system has access to a list of possible nodes. Given an input sequence of
part-of-speech tags, the system analyses each two adjacent tags, and hypothesises
a node, from the list of possible nodes, spanning these two tags. Then, all the
possible trees consisting of a putative node and its two daughters are evaluated
using Bayes’ Rule. The putative tree with the highest posterior probability is selected and placed in the lexicon. These operations are executed recursively until
a single tree spanning through the complete tag sequence is generated. These
putative trees are evaluated with Bayes’ Rule, and the authors compare the use
of two different approaches to compute the prior probability of Bayes’ Rule. The
first one uses Maximum Likelihood Estimation (MLE), where the posterior probability is estimated using an uninformative prior. The second uses the Minimum
Description Length (MDL) Principle, where the posterior probability is estimated
using an informative prior defined in terms of the compactness of the hypothesis.
The results obtained indicate that using the MDL Principle for the estimation of
SCGs generated slightly better grammars than those generated using MLE. In
spite of the good results obtained, such a learner is provided with a list of possible
nodes, and it starts from a tagged corpus, learning categories for the tags rather
than for the words, thus avoiding potential ambiguities.
Although these works investigate the problem of learning CGs with considerable success, they employ the basic AB-CG, that is not considered to be adequate
to capture natural languages. In this work a more complex variant of CG which
uses a unification-based approach is employed, and it has different learnability
properties than the works described above. Moreover, learning is within the
Principles and Parameters framework, with the use of a Universal Grammar. As
is discussed in section 2.3, learning within the PPT was shown to have positive learnability results for several criteria such as Identification in the Limit
and PAC-learning. Thus, in what follows we discuss some learning systems that
32
operate within PPT, although not necessarily using CGs.
2.2.2
Parameter Setting Learning
Even though the idea of a UG with principles and parameters is attractive, workable and accurate models of acquisition are difficult to design, and only recently
have some models been developed to study the process of parameter setting. The
problem of setting the parameters of the UG within the PPT has been addressed
by many researchers, proposing algorithms and studying the conditions under
which these would work satisfactorily, setting the parameters correctly. The goal
is to arrive at the target grammar, which is the one for which all the parameters
are appropriately set, given the evidence provided by the environment. In what
follows a brief outline of some of the learning algorithms developed is given.
One such learning algorithm is the Triggering Learning Algorithm (TLA)
[Gibson and Wexler 1994], which is error-driven, so that if it succeeds in parsing
a sentence with the current setting of parameters, then it does not do anything.
However, if it fails to parse a sentence, the TLA tries to change some of the values
of the current parameter settings, and in case this change generates a grammar
that can successfully parse the current sentence, it is adopted. Initially, the
learner chooses randomly a possible parameter setting as the starting point and
waits for triggers to come to take it from the starting point to a final state that
hopefully corresponds to the target grammar. When parse failure of a sentence is
detected, it signals for a change in parameters that is obtained by randomly selecting parameters to (re)set, and, according to the Single Value Constraint, the
learner can select only one parameter to set. The learner then selects randomly
an alternative value for the parameter and, if this change results in a successful parsing of the current sentence, then the change is adopted; otherwise it is
ignored, following the Greediness Constraint.
The TLA was studied in a word order learning task, defined by Gibson and
Wexler [1994], where the parameter space contained three parameters:
• the order of the S(ubject) in relation to the V(erb) (SV or VS),
• the order of the O(bject) in relation to the V(erb) (OV or VO) and
• the possibility of verb-second movement (+V2 or -V2).
These parameters give rise to 8 possible languages. The learner is exposed
to triggers from the target that are assumed to contain only canonical orders of
constituents (not receiving interrogative sentences, for example). Moreover, it is
also assumed that, in the triggers, objects do not appear without overt subjects
(e.g. the learner does not receive sentences with null subjects), and that the input
data is pre-analysed and is in a form that represents word order and grammatical
functions (e.g. the learner receives as input ‘Subject-Verb-Object’). Gibson and
33
Wexler then analyse the conditions in which the learner would converge to the
target. One of the problems faced by the TLA is that there are certain starting
points from which it does not converge to the target, but instead reaches a local
maximum, which is a point from which there are no triggers that can make the
learner reach the target. For example, in this 3-parameter space there are 56
possible routes defined in terms of possible starting points and targets, and, from
these, Gibson and Wexler found 6 local maxima routes for which no triggers would
take the learner to the target. Moreover, as Berwick and Niyogi [1996] discovered,
there are further 6 states that are connected to local maxima, from which the
learner could either converge to the target or end up in a local maximum. Thus,
depending on the starting point, which is randomly selected, the learner would
not be able to converge to the target. Kohl [1999] investigated the model in a
more linguistically realistic parameter space, containing 12 parameters: from the
4,096 possible grammars, 2,336 are not learnable even using the best starting
state, and, in the worst starting state, 3,892 grammars are unlearnable, with an
overall average of 3,348 unlearnable grammars.
Another problem for an error-driven algorithm like the TLA occurs when
it generates a superset of the target grammar. An error-driven algorithm only
changes parameters when a sentence that is not generated by the current grammar
is encountered. However, as a superset of the target grammar generates all the
sentences that the target generates, the algorithm will never be able to escape
this situation and reach the target grammar.
Berwick and Niyogi [1996] formalised the TLA in terms of a Markov Chain,
providing a formal description for the conditions for learnability in the hypothesis
space. They were then able to compute the probabilities of each state and to
quantify the amount of input data that a leaner needs to receive to converge
to a certain target, which can be thought of as characterising quantitatively
the convergence times required by the TLA. Frank and Kapur [1996] provide
formalisation for different concepts of trigger and determine the implications of
the use of each of these concepts in terms of learnability.
The TLA is a memoryless learner in the sense that it only uses the current
input and the current grammar to decide on the hypothesis to adopt next, and it
never stores any sentence previously encountered. One advantage of not storing
this kind of information is that it seems to be psychologically plausible, because
it does not impose an excessive memory burden, which would certainly be the
case if the learner were required to memorise every input received. On the other
hand, this characteristic allows rejected hypotheses to be revisited over and over
again, increasing the amount of input data needed in order to converge to the
target. As Brent [1996] notes, this does not seem to be plausible, since there is no
evidence that children randomly revisit neighbouring grammars. One solution for
this problem is to assume that parameters can only be reset once, which means
that, once triggering data sets a parameter, it is permanent and cannot be reset
again. The problem then is that a single incorrect trigger is enough for the learner
34
to incorrectly set its parameters, being unable to converge to the target.
In the Bayesian Incremental Parameter Setting (BIPS) learner defined
by Briscoe [1999 and in press], the parameters have probabilities associated with
each of the possible values. The defined BIPS learner is equipped with a UG and
associated parameters (represented in terms of a Generalised Categorial Grammar) embedded in a default inheritance hierarchy. It also has a parser and a
learning algorithm that updates parameter values and their associated probabilities according to the triggers provided in the data. The parameters are binaryvalued and inheritance defines a partial ordering on them. Moreover, parameters
can be initialised with absolute, default or unset values. Thus, when a triggering
sentence that is successfully parsed provides evidence for certain parameter values, these values are reinforced by incrementing the corresponding probabilities.
If a sentence cannot be parsed, the learner changes some of the parameter values
in constrained ways, and, if the changes allow the sentence to be successfully
parsed, the values used are reinforced. Such a learner is conservative, waiting for
enough evidence confirming a certain value before setting a parameter to that
value. It is also robust to a certain amount of noise in the triggers. Due to these
characteristics, the learner is also able to avoid some of the shortcomings of the
TLA, such as the problem of local maxima.
Fodor [1998] defines the Structural Triggers Learner (STL). It is a learning
system that employs the notion of structural triggers, where triggers are in the
form of tree-like structures called treelets. These treelets are obtained from the
derivation tree for a given sentence, and parameter values are also in the form
of treelets. The UG initially provides the learner with all the possible treelets,
one for each parameter value. When the learner is given an input sentence, it
parses the sentence and the treelets found in the derivation tree provide evidence
for the corresponding parameter values. When a sentence cannot be parsed,
the learner examines the partial derivation obtained and searches among the
possible treelets allowed by the UG for some that may permit the sentence to be
parsed. These are then adopted as values for the corresponding parameters. In
one version of STL only those treelets in a completely unambiguous sentence are
employed for learning. This requirement for unambiguous triggers may result in
an unreasonably large amount of sentences required for the learner to converge,
as discussed in section 2.1.1.
In the Variational Model [Yang 1999], language acquisition is viewed as
the task in which a population of grammars compete in a Darwinian selectionist
process. The learning model is equipped with a population of grammars, corresponding to the possible variations among languages, and where each grammar is
associated with a weight. The learner is given sentences as input, and the learning algorithm proceeds in a selectionist manner, rewarding those grammars that
can successfully analyse the input and penalising those that cannot. Language
acquisition is guided by evidence that disambiguates the target grammar from
competing ones, and the learner converges to the target when the composition
35
and distribution of the grammar population stabilise.
2.3
Learning Paradigms
In this section we discuss three learning paradigms starting with Identification
in the Limit and PAC-learning, which are two criteria for the learner’s success,
and finishing with Minimum Description Length which is an algorithmic way for
defining learners.
2.3.1
Identification in the Limit
Gold, in his influential paper [Gold 1967], defines the problem of identification
in the limit, where the learner is asked to infer a particular target concept, given
an enumeration of hypotheses and a sequence of positive and negative examples
which may contain repetitions.
The learner then performs the learning task using induction by enumeration, where all the hypotheses in the enumeration that are not consistent with
the set of examples seen so far are eliminated, from left to right, up to the first
consistent hypothesis. At each new example received, the learner repeats this
process, until a hypothesis in the enumeration is found that is identical to the
target and that will be consistent with any new example. At this stage, the
process is said to have converged.
In general terms, the idea is that the learner is considered successful when it
eventually stabilises on a hypothesis that corresponds exactly to the correct one,
regardless of the order of presentation of the examples.
As Bertolo [2001] remarks, in one sense the definition of identification in the
limit is too idealised for human language learning, since it assumes that the
information provided for the target language is complete and perfectly reliable
and does not consider noise, ambiguity and incomplete information. Moreover,
this definition is also too liberal, because it does not impose any restrictions
about the number of examples and the time that the learner needs to make
the identification. It only requires that this identification occurs eventually. Li
and Vitanyi [1995] observe that, if significant time restrictions are added to the
inductive model, almost all concepts are made not learnable, except some trivial
ones, under these requirements. In any case, the class of grammars consistent
with the PPT is learnable under this criterion, as discussed by Bertolo [2001].
2.3.2
PAC-Learning
Probably Approximately Correct (PAC) learning [Valiant 1984],
[Li and Vitanyi 1993], [Li and Vitanyi 1995] is an alternative criterion for
the success of the learner that is more adequate than identification in the limit.
36
It requires the learner to identify a hypothesis with high probability that is very
close to the target concept, based on a reasonable number of examples. In this
framework every language has a particular probability distribution according
to which the examples are given to the learner. The idea is that the learner
is successful if it can produce a hypothesis that would misclassify only the
sentences that are unlikely to be given as part of its learning environment. The
speed of convergence depends on how small the chance of error is required to
be, so that the smaller the chance of error, the larger the amount of examples
needed and the longer the convergence time is going to be.
In PAC-learning not all the examples will be presented to the learner and, as
a consequence, the target concept cannot be precisely inferred and can only be
approximated. Furthermore, the difference between the inferred hypothesis and
the target can be expressed in terms of the probability of the set of examples on
which these two disagree.
However, even though PAC-learning is not as stringent in its requirements
as identification in the limit, the application of the PAC-learning model led to
more negative than positive results. It seems that its requirements are still too
strict for the learner. Nonetheless, as Li and Vitanyi [1995] observe, in practical
learning situations, what happens is that the class of probability distributions
can be restricted, the learners can usually ask questions, or the teachers can be
helpful, among other things that can make the learning task less difficult for the
learner. Once again, any finite class of languages consistent with the Principles
and Parameters Theory is PAC-learnable [Blumer et al. 1987].
2.3.3
Minimum Description Length
The Minimum Description Length (MDL) Principle ([Rissanen 1989] and
[Li and Vitanyi 1995]) is a method for designing learners, thus differing from
identification in the limit and PAC-learning that are formal criteria of success
to determine whether a given learner has performed well. In MDL the task of
the learner is, given a sequence of examples, to choose a hypothesis that can
be described concisely and at the same time does not make too many errors in
relation to these examples. Therefore, given an enumeration of hypotheses and a
set of examples, the MDL Principle states that the best hypothesis to infer from
the data (the set of examples) is the one whose description is compact in length
and that explains the examples well. MDL incorporates the idea that by only
considering hypotheses that model the data well, one gets a theory with a more
complex description where the number of misclassified examples decreases. However, it also means that this theory will probably overfit and will not predict well
any unseen data. On the other hand, by only considering compact hypotheses,
the description of a theory may be so simple that it will probably model the data
badly. Thus, when evaluating hypotheses it is often the case that greater accuracy
is achieved in the description of new data with a small but imperfect theory, than
37
with a theory that perfectly describes the known data [Quinlan and Rivest 1989].
The MDL Principle can be incorporated into Bayesian Learning, which is
employed as the basis of some language learning systems. Bayes’ theorem is
defined as:
P (H|D) =
P (H)P (D|H)
P (D)
where:
• the term P(H) is the prior probability, which represents the learner’s
belief in the hypothesis H. If the prior is accurate, it will give higher probabilities to hypotheses that are close to the target than to the ones that are
further away,
• P(D|H) is the likelihood probability and it represents how well the hypothesis H encodes the data D,
• P(D) is the probability of the data, and
• P(H|D) is the posterior probability. It can be seen as the combination of
the prior and likelihood probabilities, so that one tries to find a hypothesis
that maximises these two terms given the data.
The prior probability can be thought of as a bias or background knowledge the
learner has, that helps searching for the target hypothesis. When the learning
process starts, the prior probability is the only source of information for the
learner and, as such, dominates the value of the posterior probability. However,
as the learner receives more and more input data, it also relies on the data to
perform the search. In the limit, it is the data (the likelihood probability) that
dominates the posterior probability regardless of the initial belief of the learner
(the prior probability). By helping to guide the search, an informative prior
can make the convergence faster, which is especially important because there is
usually only a limited amount of data available to the learner. However, it is
not always easy to find an informative prior. One commonly used approach is
to assume an uninformative prior, which results in a Maximum Likelihood
Estimator (MLE). However, this approach leads to the problem of overfitting,
where the best hypothesis is the one which only accounts for the data seen so
far, predicting poorly any unseen data. A better approach is to use an MDLstyle informative prior, using the notion of complexity of hypotheses, such that
each hypothesis is evaluated in terms of its length and smaller hypothesis are
preferred. Thus, the longer the length, the more complex the hypothesis is.
This prior favours smaller (more compact) hypotheses by assigning them higher
probabilities. The likelihood probability, on the other hand, prefers hypotheses
38
that model the data well. Given that a Bayesian learner is searching for a theory
with high posterior probability, it needs to find the most compact hypothesis that
describes the data well, balancing the prior with the likelihood probability. In
addition, as Quinlan and Rissanen [1989] note, the great contribution of MDL is
that it provides the learner with the conceptually simpler problem of computing
the lengths of the hypotheses.
MDL is a more practical paradigm than either Identification in the Limit
and PAC-Learning, and it has been successfully applied in a number of learning
systems, like those in [Chen 1996], [Osborne and Briscoe 1997], [Stolcke 1994],
[Briscoe 1999]).
2.4
Summary
In this chapter an overview of some relevant work on human language acquisition and on computational learning systems was presented. The UG is a useful
concept that provides the core knowledge that the learner needs in order to acquire a particular language. By doing this, the UG restricts the hypothesis space
that the learner needs to consider in the search for the target grammar. It is
the responsibility of the learning algorithm to set the values of the parameters
appropriately in order to converge to the target grammar based only on positive
evidence about a particular language. A subset of this positive evidence consists
of triggers which are the linguistic data that give evidence for the parameter
values. In terms of learning, an efficient search strategy needs to be conducted,
because even though the space allowed by the UG is more restricted, it is still too
vast for an enumerative search to find the target grammar in a reasonable amount
of time. Thus, in this work, the UG is going to be used in conjunction with an
MDL interpretation of Bayes’ Rule to direct the search for the target grammar:
while the UG restricts the hypothesis space to only those grammars that are
consistent with the principles and parameters defined, the MDL Principle guides
the search in this hypothesis space by leading the learner to look for a compact
hypothesis that models the data well. The Bayesian Incremental Parameter Setting learner defined by Briscoe [1999] is the learning model adopted for this work.
It is adapted to learn a Unification-Based Generalised Categorial Grammar from
child directed sentences annotated with logical forms. Such a model provides the
testing grounds for linguistic and psychological theories of language acquisition
and can potentially provide several insights into language acquisition.
39
Chapter 3
Grammar Encoding
In a lexicalised linguistic formalism, like Categorial Grammar (CG) or HeadDriven Phrase Structure Grammar (HPSG), the lexicon is the focal point, with
most of the information being located there and with the syntactic component
being drastically reduced. In such theories different kinds of linguistic information are described in the lexicon. Thus, a lexical entry can contain, for example,
information about the orthography, syntax and semantics of a word. These theories are said to be ‘sign-based’, since they adopt Saussure’s idea that a sign
is composed by the association of sound, form and meaning ([de Saussure 1916]
and [Pollard and Sag 1987]). The issue of how to organise lexical information is
essential, since the burden of linguistic description is concentrated in the lexicon.
Thus, if lexical entries are organised as unrelated lists, there is a significant loss
of generalisation and increase in redundancy.
In this chapter we discuss some grammar encoding techniques to organise
lexical information. The first one is the use of inheritance hierarchies, in section
3.1. It is followed by a discussion of the use of type systems in section 3.2. The use
of default specifications in the representation of linguistic knowledge is discussed
in section 3.3 and the use of lexical rules in section 3.4. Finally, the last two
sections provide brief descriptions of the specific versions of default unification
operations that are employed in this research.
3.1
Inheritance Hierarchies
When building a lexicon, a lot of the information described in one lexical sign
will also be contained in other signs. For example, many of the properties of
the verb ‘like’ are also shared by the verb ‘love’: both are transitive verbs, both
have past form ending in ‘ed ’, both have third person singular form ending in ‘s’,
and so on. These properties are also shared by a great number of other verbs.
As a consequence, a sensible alternative is to define the information common
to a group of signs just once, rather than repeat it in each of these signs, and
40
use inheritance hierarchies to propagate this information. Inheritance hierarchies
allow us to do that by providing representations that are able to capture linguistic
regularities about classes of items that behave similarly.
The organisation of these objects into class and subclass relations results in a
hierarchical structure where linguistic regularities are encoded near the top of the
hierarchy; nodes further down the hierarchy are used to represent sub-regularities.
As a consequence, all the properties associated with a given class are inherited
by all its subclasses and added to the properties defined as idiosyncratic in each
subclass. If each subclass in an inheritance hierarchy has only one parent class
from where all the properties are inherited, it is classified as a single inheritance hierarchy. On the other hand, if a given subclass inherits properties from
more than one parent class, it is in a multiple inheritance hierarchy. In this
case, care must be taken because it is possible for a class to inherit contradictory
information from different parents. Furthermore, if all the properties associated
with a parent class are inherited by all its subclasses without exceptions or possibility of change, a hierarchy has monotonic inheritance. If, however, the
properties specified at a given class take precedence over those inherited from its
parent classes, the class has nonmonotonic inheritance. This is also known
as default inheritance, since the value for a particular property in a subclass is
inherited by default from its parent classes, unless it is specified in the subclass
itself, in which case its specification will then take precedence over the inherited
value. Monotonic single inheritance hierarchies are easy to build and to understand, but they are not really suited for the description of natural languages,
since subregularities and exceptions cannot be easily or straightforwardly defined
[Daelemans et al. 1992]. More suited for the description of natural languages are
multiple inheritance hierarchies, where different hierarchies can be defined for different properties, and nonmonotonic inheritance hierarchies, where the overriding
mechanism can be used to allow for exceptions.
In terms of applications, inheritance in a unification-based grammar processing system can be found in PATR, where, according to Shieber [1986], the use
of lexical templates corresponds to a language for defining multiple inheritance
hierarchies. One of the theories that has made use of inheritance networks is
HPSG. Pollard and Sag [1987] treat the lexicon as a monotonic multiple inheritance hierarchy, where information common to a class of items is inherited by its
subclasses, shown in figure 3.1 [from Pollard and Sag 1987, p. 206]. Flickinger
et al. [1985] define the lexicon in terms of multiple inheritance hierarchies. They
distinguish between two modes of inheritance:
• in the normal mode locally declared values override more general values
inherited from classes higher up in the hierarchy,
• in the complete mode of inheritance the more general values defined in
the hierarchy take precedence over the more specific ones.
41
BC( $ D! "$ ! %
>[email protected]
H 19
E;F
B! "IB(
=J4
C"! E
G3G3
! ! ! " ! #
! " #$
! ! ! %
! #
&'!
! " 'D! $ ! K
"#$
! ! ! %
&('!
*)+*0
JL
4M/;22L
, 1 -32, 0
2* 4M2/
L2*/
)+*, -
9N<8.
8229
./0
, 1 -32
451 62
72, 1 262
:+2/;8<*=2
Figure 3.1: Pollard and Sag’s Hierarchy
Flickinger and Nerbonne [1992], in their analysis of easy adjectives, also highlight the advantages of using inheritance hierarchies for lexical representation,
concentrating on its ease of maintenance and modification. Other theories
that use multiple inheritance networks are Unification Categorial Grammar
[Moens et al 1989] and Word Grammar [Hudson 1990]. DATR is an implemented
theory of lexical knowledge representation incorporating multiple default inheritance and, although it requires orthogonality, Evans et al [Evans et al. 1993]
show how to encode some kinds of prioritised inheritance.
3.2
Types
In addition to inheritance hierarchies, a typing system can also be used to structure information [Aït-Kaci 1984], [Carpenter 1990], [Carpenter 1992]. Thus, information is typed and structured according to a partial ordering on the types
defined. Types place appropriateness conditions on classes, and each element of
a class must follow these conditions. The typing system determines which structures are mutually compatible and which attributes can occur for a given class. It
can be used to define an inheritance hierarchy, where it imposes appropriateness
conditions that are monotonically passed to all the subtypes of the type that
42
! "# !
%$"# !
Figure 3.2: Fragment of a Type Hierarchy




















nominal-m-feats



PRON : boolean


WH : boolean



LOC : boolean




agr


 NUMBER : number  
AGR :  PERSON : person  


GENDER : gender 
Figure 3.3: Specification of a Complex Feature Structure
introduced those conditions.
Figure 3.2 shows a type system defining a hierarchy. In the examples that
follow, attributes are displayed in uppercase letters and values in lowercase bold
face, e.g. cat and s, respectively. The value of an attribute needs to be a type in
the hierarchy, and it can also be marked as reentrant with another attribute. top
is the most basic type defined and is the common supertype of all the types and,
inside feature structures it is represented as >. Boxed alphanumeric symbols (e.g.
1 ) are used to indicate reentrancies, or structure sharing between substructures,
with the coindexation being used for representing substructures that are reached
by different sequences of attributes. Throughout this document, only the relevant
information is shown in the figures for reasons of clarity.
The type hierarchy defines a partial order on the types. The more specific
the type, the lower in the hierarchy it is defined. A more specific type has all the
information contained in a more general supertype, with possibly some additional
information.
Each type in a hierarchy has an associated feature structure (FS) that is
appropriate to it. If an FS is basic, it has an atomic value that corresponds to
one of the types defined, as can be seen in figure 3.3 for the attributes pron,
wh and loc, with value boolean. If the FS is complex, it provides values for
one or more attributes, which in their turn, can be either basic or complex, as
in the attribute agr (figure 3.3). The FS associated with a type acts as a
constraint that defines what is appropriate for that type, and it is inherited by
all its subtypes. Thus for the type agr, the attributes person, number and
gender are appropriate attributes.
43




















nominal-m-feats



PRON : true


WH : false



LOC : false




agr


 NUMBER : singular  


AGR :  PERSON : 2





GENDER : gender
Figure 3.4: Specification of Another Complex Feature Structure
Typed feature structures (TFSs) can be regarded as being ordered by specificity, so that the FS shown in figure 3.4 is more specific than that shown in
figure 3.3. The unification of two typed feature structures results in the most
general feature structure that retains all the information contained in each one
of them. There is also a subsumption relation between TFSs: a more general
one subsumes a more specific one. For example, the FS shown in figure 3.3
subsumes that in figure 3.4, since the former is contained in the latter.
In terms of applications of types, Sanfilippo [Sanfilippo 1993] defines a system
of verb types for English with a hierarchy of semantic types, a hierarchy of syntactic types, and a hierarchy of signs. The signs combine information from the
syntactic and semantic types by coindexing the subcategorised elements and the
semantic arguments. The theory of lexical organisation outlined by Pollard and
Sag [1987], shown in figure 3.1, can also be defined using a hierarchy of types,
where all the types in the subcat hierarchy have an attribute subcat encoding
a list of subcategorised elements. The analysis of easy adjectives proposed by
Flickinger and Nerbonne [Flickinger and Nerbonne 1992] can also be described
in terms of types organised in a nonmonotonic inheritance hierarchy.
3.3
Defaults
The use of inheritance hierarchies to structure linguistic information, allows generalisations about classes of items to be economically expressed. Moreover, inheritance based on typing provides a way to define appropriateness conditions on
classes of linguistic objects. However, if the inheritance hierarchies are defined as
monotonic and absolute systems, like Pollard and Sag’s [1987], they fail to make
use of defaults which would significantly reduce redundancy in lexical specifications and would enable them to straightforwardly express sub-regularities.
As several authors have highlighted, defaults are important in the representation of linguistic knowledge, providing linguistically adequate descriptions for natural language phenomena [Gazdar 1987], [Daelemans et al. 1992], [Bouma 1992],
[Krieger and Nerbonne 1993], [Briscoe 1993].
Among the characteristics that make the use of multiple default inheritance
44
networks so appealing, it is possible to cite [from Daelemans et al. 1992]:
• parsimony - inheritance lexicons should be smaller than the full-entry counterparts,
• ease of maintenance - changes or corrections are localised to a few nodes,
• uniformity - different levels of linguistic descriptions are encoded in the
same manner and are subject to the same rules of inference,
• modularity - different taxonomies can apply for different levels of description,
• interaction - properties at different levels of description interact with one
another,
• the ability to capture linguistic generalisations,
• the ability to capture linguistic subregularities and exceptions with the
overriding mechanism,
• the ability to provide non-redundant representations.
Defaults can be viewed as a restricted form of nonmonotonicity that
may be used only for lexical generalisations and the defaults can be configured to act as monotonic constraints outside the lexicon [Bouma 1990],
[Krieger and Nerbonne 1993]. Default networks allow properties to be incrementally true, so that things can be considered true by default until further evidence
is discovered that indicates that they are false (and they are then overridden).
Moreover, the use of default inheritance hierarchies is not only motivated for
considerations of parsimony and conciseness, but also by psychological considerations, since speakers recognise systematic relationships among words, as pointed
out by Sag and Wasow [1999].
An example of the use of defaults for linguistic description is found in [Lascarides and Copestake 1999] in a treatment of modals that uses defaults to allow
ought to be an exception to the general class of modals. Modals can be inverted (‘can’ in ‘Can I use the car? ’), can be negated without requiring the
presence of ‘do’ (‘will ’ in ‘I will not go to the theatre tomorrow ’), and can have
the contracted negated form (‘shouldn’t’ in ‘He shouldn’t stay there longer than
five days’). The specification of the modal type is shown in figure 3.5 [from
Lascarides and Copestake 1999]. In this figure, the non-default (or indefeasible)
value of an attribute is separated with ‘/’ from the default (or defeasible) value,
so that they are represented as Indefeasible/Defeasible. This specification can
be abbreviated to Indefeasible, if Indefeasible = Defeasible and abbreviated to
/Defeasible if >/Defeasible, with > (top), being the most general type. This notation follows Lascarides et al. [1996] and is adopted throughout this document.
45
















modal

SYNSEM





: 





HEAD AUX
:
VAL COMPS

true

: h

 HEAD VFORM : /bse 


VAL COMPS : hi










i




Figure 3.5: Constraint on Type modal



modal

ORTH : could
Figure 3.6: Lexical Description for could
Figure 3.5 shows the definition of some syntactic characteristics of a modal verb
in the synsem attribute. Firstly, it is a verbal category which has the behaviour
of auxiliary verbs, encoded in synsem:head:aux:true. Moreover, in terms of
valence, encoded in the val attribute, a modal verb is specified as subcategorising for a verb phrase that is in the base form (synsem:val comps:<head
vform:/bse>) and has an empty complements list (synsem:val comps:<val
comps:<>>). This is the type associated with most modals, such as ‘could ’,
which is encoded as shown in figure 3.6. Since ‘could ’ does not introduce any
other constraint, it inherits all the information encoded in the modal type, without exception, as can be seen in figure 3.7, where ‘could ’ is shown expanded.
Ought, on the other hand, has the syntactic behaviour of modals in most respects,
but unlike most modals it requires a to-infinitive verb as a complement, being an
exception to the general case. Thus, in its lexical entry, ought defines the requirement for an infinitival verb phrase (synsem:val comps:<head vform:inf >),
as shown in figure 3.8. Since the modal type specifies the form of the subcategorised verb phrase as default information (synsem:val comps:<head
vform:/bse>) (figure 3.5), even though ‘ought’ inherits most of the information from this type, it also overrides this default information, being expanded
as shown in figure 3.9.



















modal
ORTH : could

HEAD AUX

SYNSEM




: 






:
VAL COMPS
true

: h

 HEAD VFORM : /bse 


VAL COMPS : hi
Figure 3.7: Expanded Feature Structure for could
46













i















modal
ORTH : ought

SYNSEM VAL COMPS
: h
"
HEAD VFORM : inf
#








i

Figure 3.8: Lexical Description for ought



















modal
ORTH : ought

HEAD AUX

SYNSEM




: 






:
VAL COMPS
true

: h

 HEAD VFORM : inf 


VAL COMPS : hi













i




Figure 3.9: Expanded Feature Structure for ought
In the case of modal verbs, the use of default specifications provides a way of
capturing the generalisation that most modals take a base form complement. At
the same time, it licenses the integration of exceptions, such as ought that takes
an infinitival complement.
This is only one of the possible applications for defaults in the definition of
linguistic phenomena. Defaults can also be used for encoding inflectional morphology [de Smedt 1984], [Flickinger et al. 1985], [Briscoe and Copestake 1999],
and they can be used in the description of rules, schemata or constructions [Gazdar 1987], [Lascarides and Copestake 1999], among other applications.
Throughout these and other works1 , defaults have been successfully used to express the idea that natural languages have general constraints, but that there are
usually exceptions to these constraints.
3.4
Lexical Rules
Another mechanism that can be used to further reduce redundancy in lexical
specification is that of the lexical rule. Lexical rules are used to generate a lexical
entry based on information from another entry. The lexicon can then be divided
into two groups of entries: basic and derived entries, and lexical rules can be
used to construct a predictably related derived entry from a basic or another
derived entry. In a lexicalist approach to grammar, they have a major role of
capturing lexical and morphological generalisations, such as plural formation and
1
For an overview of the use of defaults see [Gazdar 1987], [Daelemans et al. 1992],
[Krieger and Nerbonne 1993],
[Lascarides et al. 1996b],
[Malouf 1998],
and
[Sag and Wasow 1999].
47











base
PHON ": 1
SYN : LOC : SUBCAT
SEM : CONT : 4




#


3




:

3rdsng
PHON ": f3rdsng( 1 )
7
→
SYN : LOC : SUBCAT
SEM : CONT : 4











:



#


3




Figure 3.10: HPSG Third Singular Verb Formation Lexical Rule


base
PHON
:
1



7→  3rdsng
PHON
:
f3rdsng(
1 )


Figure 3.11: Abbreviated Form of the Lexical Rule
verb alternations.
A common interpretation of lexical rules is as conditional relationships between lexical entries. Thus, a lexical rule is applied to an input lexical entry
to generate a new entry that is related to the input in terms of form, syntactic
category and semantics. For instance, lexical rules can add morphological affixes
to lexical entries, e.g. by generating the third person singular form of a verb
from its base form. In this way, with an input and an output specification for
lexical rules, when a lexical entry unifies with the input or antecedent description of a rule, a new derived entry is created by copying specified elements to
the output or consequent description. The output will be defined in terms of
idiosyncratic information that is copied or computed from the particular input
lexical entry and predictable information that is available via inheritance links.
In these rules, coindexations are usually interpreted as copying operators - as
opposed to their usage as reentrancies within a sign - copying information from
the input to the output of a rule. As an example, the rule of third singular verb
formation is shown in figure 3.10 [from Pollard and Sag 1987]. This rule specifies
that the input structure, in the left hand sign, should be a verbal lexical entry
in the base form, whose syntactic and semantic characteristics are copied to the
output structure (syn:loc:subcat: 3 , and sem:cont: 4 ), in the right hand
side. This rule also establishes that the orthography of the output structure is
determined by a function (f3rdsng) that takes the orthographic form of the input
and returns an inflected word corresponding to the third person singular form
(phon:f3rdsng( 1 )). However, in terms of notation, it is common in the literature for this rule to be abbreviated to the one shown in figure 3.11, with the
elements that are to be copied unchanged from input to output left unstated.
Lexical rules are a widely used mechanism in lexical representation. For instance, Flickinger et al [Flickinger et al. 1985] use lexical rules as one of the mechanisms for eliminating redundancy in lexical representation. They also combine
the use of inheritance hierarchies which, among other things, allow them to specify the domain to which a lexical rule is to apply. These two mechanisms are
48
3rdsg
7
PHON
base →









: 
3RDSNG
FUNCTION : f3rdsng
ARGS : h>, 1 i
:
1








Figure 3.12: Reinterpreted Third Singular Verb Formation Lexical Rule











base
PHON

: 
FUNCTION :
ARGS : hlovei
3RDSNG :
SYN LOC SUBCAT


NPi
: h











Figure 3.13: Lexical Description for the Base Form of love
also used for blocking, where the application of a lexical rule to create a regular
form for a particular word is prevented by the existence of an irregular form of
that word. This is achieved by allowing a lexical entry, in its specification, to
explicitly define its appropriate irregular form. Sanfilippo [Sanfilippo 1993] also
employs lexical rules, but constrains their applications by specifying in the lexical
entries a list containing the rules that can be applied to them. In this way, a
lexical rule will only be applied to an entry that contains that rule name in the
list of possible rules. Lexical rules are also widely used by Sag and Wasow [1999],
which, among other rules, define those for capturing inflectional morphology.
As pointed out by Briscoe and Copestake [1999], the approach of treating
lexical rules as a homogeneous class introduces a series of problems. For instance,
the use of lexical rules to perform arbitrary manipulations of lists results in the
possibility of generating any recursively enumerable language [Carpenter 1991],
posing no limits on expressivity.
An alternative approach suggested by Briscoe and Copestake [1999] is to
define lexical rules using asymmetric default unification. By using asymmetric
default unification the output structure is identical to the input, except where
otherwise specified in the output. This operation allows the carrying over of
consistent information from the input to the output structures. This can be seen
in figure 3.12 [from Briscoe and Copestake 1999] where the third person singular
verb formation rule is reformulated in terms of asymmetric default unification.
This rule specifies that the third person singular form of a verb is obtained
from a base form input (base, in the left hand side of the rule). In the right hand
side of the rule, a function applied to the orthography of the word generates the
required form, in the attribute 3rdsng. When this rule is applied to a lexical
item, like the word ‘love’ shown in figure 3.13, the input, shown in the right
hand side, is treated as defeasible and the output, shown in the left hand side, as
indefeasible, figure 3.14.
49
3rdsg



 PHON














<
FUNCTION : f3rdsng   u
: 
s



ARGS : h>, 1 i


3RDSNG : 1


base
PHON

: 
FUNCTION :
ARGS : hlovei
3RDSNG :
SYN LOC SUBCAT


NPi
: h











Figure 3.14: Asymmetric Default Unification of Output and Input Structures











3rdsg
PHON

: 
FUNCTION : f3rdsng
ARGS : hlove, 1 i
3RDSNG : 1
SYN LOC SUBCAT
NPi
: h











Figure 3.15: Application of the Third Singular Verb Formation Lexical Rule
The result shown in figure 3.15 contains all the information from the indefeasible output specification and also all the consistent information from the defeasible
input specification. Thus, if the input contains information that is inconsistent
with the output, then this information is lost. However, if the output contains
information that is incompatible with the input, this information survives. In
terms of linguistic applications, lexical rules based on asymmetric unification are
used in the treatment of dative constructions proposed by Briscoe and Copestake [1999]. This treatment captures the idea of a family of dative constructions
[Goldberg 1995] with the same syntactic and related semantic properties.
By generating a lexical entry based on information from another entry, lexical
rules help to reduce redundancy in lexical specification. Moreover, asymmetric
default unification successfully allows the encoding of lexical rules by only defining
what is to be changed and by automatically carrying over what is to remain unchanged from the input to the output form. The use of asymmetric unification in
the specification of lexical rules results in a more restricted mechanism than that
used in conventional lexical rules, since it cannot arbitrarily ‘rearrange’ material
between the input and the output structures [Briscoe and Copestake 1999].
3.5
Asymmetric Default Unification
In this section, we describe the particular version of asymmetric default unification used in this work to implement lexical rules.
In the asymmetric default unification of two FSs the first one is treated as an
indefeasible structure and the second one as defeasible. The result of the asymmetric unification is equal to the indefeasible FS but also incorporates compatible
information from the defeasible FS. This operation is non-deterministic and may
generate more than one possible resulting structure. When this happens, the
50
result is taken to be the generalisation of the unified structures, implementing
Skeptical Default Unification as defined, for example, by Carpenter [1993].
In this way, the skeptical default unification of two FSs only maintains default
information that does not conflict in any way with the non-default information,
and this is the information that can be found in every possible resulting structure.
<
The skeptical unification, us , of two structures is shown in figure 3.16. In this
figure, true and false are types in the hierarchy shown in figure 3.2, being both
subtypes of boolean and incompatible for unification. As the generalisation of
two types is their lowest upper bound in the hierarchy, these two types generalise
to their supertype boolean. The asymmetric unification of the two FSs in figure
3.16.a generates two possible structures, the first one ignoring the reentrancies
and the second one maintaining them. Then these need to be generalised for a
skeptical unification, as in figure 3.16.b, where both the value for F, which is
true in the two FSs, and the value for H, which is false in both of them, are
kept in the generalisation of the two FSs. However, as the value of G is false in
one FS and true in the other, in their generalisation G has value boolean which
is the common supertype of true and false.

<
F : true

a. G : boolean  us
H : false






F :
G :
1
1

false 
b.
=
=













 

F : true   F : 1 true 




G : false ,  G : 1




H : false
H : false






F : true

G : boolean 
H : false
Figure 3.16: Skeptical Asymmetric Default Unification
This version of skeptical unification is extended by Briscoe and Copestake
[1999] for typed feature structures. Thus, the unification of two TFSs is only
allowed if the resulting TFS has only attributes that are appropriate for that
particular type.2
3.6
Symmetric Default Unification
In this section we describe the version of symmetric default unification used
to implement the default multiple inheritance network of types that represents
linguistic information throughout this work.
yadu [Lascarides et al. 1996b], [Lascarides and Copestake 1999] is an order
independent default unification operation on typed feature structures. yadu can
be regarded as a default operation that tries to incorporate the maximal amount
2
A more detailed description of asymmetric default unification can be found in
[Carpenter 1993] and [Briscoe and Copestake 1999].
51
of information given its priority. The information is encoded in features that
have both non-default and default values. In order to distinguish non-default
from default information, yadu uses an extended definition of TFSs called typed
default feature structures (TDFSs). A TDFS is composed of:
• an indefeasible part (I ), which contains the non-default information,
• a defeasible part (D), which contains the default information, and
• a tail T, which is composed of a set of pairs where the first element is a
path or path equivalence and the second is the associated type, recording
unification history.
As a consequence, during default unification, non-default information can
always be preserved and only consistent default information is incorporated into
the defeasible TFS. Another important point is that default unification of two
FSs is deterministic, always returning a single
value.
<>
<>
There are basically three operations: u , DefFS and DefFill. u can be informally defined as an operation that takes two TDFSs and produces a new one
where:
• the indefeasible part is the result of unifying the indefeasible information
defined in the input TDFSs, and
• the tail results from the union of the tails, with all the elements that are
incompatible with the resulting indefeasible part I removed.
The defeasible part of the TDFS is calculated using the operation DefFS,
which defines the defeasible part as the result of unifying the indefeasible TFS
with the maximal set of compatible values of the tail, in order of specificity (given
by the position of the associated types in the hierarchy). As tails may contain
conflicting information, this operation is used in order to know which elements
in the tail ‘win’. To compute
the result of the default unification of two FSs, it is
<>
first necessary to apply u to compute I , the indefeasible FS, and T , the tail, and
then to apply DefFS to compute D, the defeasible FS, as shown in the following
example.
Given that t0 @ t (t0 is more specific than t) and that > represents the most
general type in the hierarchy, the symmetric default unification of two FSs:
1.







t0
 <>  t

F : >/a  u  F : >/ 1
G : >/ 1
G : >/b






is computed by unifying the indefeasible parts of the two FSs:




0
t0

t

t

• I = F : >  u  F : >  =  F : > 
G : >
G : >
G : >







52
and by taking the set union of the two tails:

:
• T = {h F : a ,t0 i, h G : b ,t0 i, h  F
G :
1
1


,t i}
Then it is possible to calculate the resulting defeasible structure:


!
!
0

t
 < < 


: 1 


F : a , G : b
2. D12 = t
us  F
 F : >  us


G : 1
G : >
!


= t
=










t0
 <
:

u

F : a  s F
G
:
G : b
1
1


t0

F : a 
G : b

where the defaults are added in order of specificity of types, with the constraints
introduced by t0 (F:a, G:b) being added first and then the constraints introduced
by t (F: 1 , G: 1 ). As the latter are incompatible with the resulting FS, they
are ignored.
The third operation, DefFill turns default specifications into non-default information. It has a TDFS as input and returns a TFS by simply taking the
defeasible TFS
constructed
by DefFS. Taking the previous result we have that:


0
t


DefFill( F : >/a  {h F : a , t0 i, h G : b , t0 i, h F : 1 , ti, h G : 1 , ti} )
G : >/b
t0

= F : a 
G : b






The DefFill operation can be executed, for example, at the interface between
the lexicon and the rest of the system. This operation has to be applied to all
the defaults that are only used in the grammar to capture lexical generalisations, and they have to be made indefeasible after the lexicon; otherwise they
may be overridden during later processing. These defaults are considered to
be non-persistent defaults. yadu also provides the possibility of defining defaults that are going to contribute to the output of the grammar: the persistent
defaults. These defaults are marked to persist outside the lexicon with the p
operator [Lascarides et al. 1996b]. This operator has already been shown to be
important for keeping lexically encoded semantic defaults until discourse processing, where they can be overridden by discourse information when appropriate
[Lascarides et al. 1996a].
Furthermore, yadu supports the definition of inequalities. The inequality
relation defined between two nodes is a restricted form of stating negative information in terms of FSs, as described in [Carpenter 1992]. Thus, inequalities are
a way of defining that two FSs are not equivalent, so that they never become
identical after an inequality is encountered. Inequalities can be used to override
53
default reentrancies in the unification of two types when no conflicting values are
defined in the types involved [Lascarides and Copestake 1999].
By using yadu, defaults become an integrated part of the typed feature structure system implemented. It achieves the perspicuity, declarativity and expressivity that are familiar from unification-based approaches to non-default inheritance.3
3.7
Summary
In this chapter several mechanisms for grammatical implementation were discussed. They all contribute to the construction of a structured lexicon that
is succinct and avoids redundancy in the specification of linguistic information.
They allow the representation of generalisations present in natural languages,
while also describing subregularities and exceptions that do not fully follow the
general case, but nonetheless have many properties in common. Finally, the two
versions of default unification used throughout this work were presented.
3
A more detailed description of yadu can be found in [Lascarides and Copestake 1999].
54
Chapter 4
Unification-Based Generalised
Categorial Grammar
This chapter provides a description of the grammar implemented in the scope
of this research. The grammar is formalised as a Unification-Based Generalised
Categorial Grammar, but the description of types provided is meant to be compatible with several theoretical approaches. By using a radically lexicalised theory of grammar, the lexical types defined contain a great amount of information.
Therefore, the use of a different framework would only require the removal or
translation of the linguistic information from the lexical types to another component of the grammar.
This chapter starts with an introduction to Categorial Grammars. Then, in
section 4.2, Unification-Based Generalised Categorial Grammars, the particular
version of CGs being used in this work is presented, followed by a description of
the set of rules, in section 4.3, and by an analysis of the coverage obtained by
such a grammar, in section 4.4. Section 4.5 provides a detailed account of how
the implemented grammar is used to formalise a theory of the UG and section
4.6 describes the corpus used to set the parameters of the UG.
4.1
Categorial Grammars
Categorial Grammar [Ajdukiewicz 1935], [Bar Hillel 1953] and [Lambek 1958] is
a lexicalised grammatical formalism. It is characterised by regarding language in
terms of functions and arguments and by allowing the representation of semantics
directly in syntax with each rule of syntax being a rule of semantics.
As a lexicalised formalism, the syntactic behaviour of any item is directly
encoded in the lexicon, as the item’s lexical category specification. In this way,
practically all the information about how words can be combined into phrases
is present in their lexical entries: a linguistic entity is described in terms of
categories with which it can combine and the result of this combination. For
55
example, the attributive adjective big has its syntactic behaviour encoded as
N/N, meaning that it needs an N to its right, denoted by ‘/N’, to form a noun
‘N’. As a consequence, there is no need for a separate grammar rule component
that describes the constituents that need to be combined and the constituent
resulting from the combination. Instead, CGs have a small set of rules that are
applied to the categories corresponding to the words of a given sentence to check
the legality of the sentence and to build its semantic interpretation.
A CG is composed of a lexicon and a small set of rules. Many versions of
CGs have been defined, and they differ in terms of the set of categories defined
and/or in terms of the set of rules used (e.g. [Lambek 1958], [van Benthem 1988],
[Morrill 1987], [Moortgat 1988], [Carpenter 1998] and [Steedman 2000]). This
discussion starts with a description of AB-CG, the basic CG, and is followed by
a description of other configurations that extend either the set of categories, or
the set of rules, or both.
4.1.1
AB-Categorial Grammar
The basic version of CG, known as AB-Categorial Grammar (AB-CG), or classical
Categorial Grammar, is defined by Ajdukiewicz [Ajdukiewicz 1935] and Bar-Hillel
[Bar Hillel 1953]. In CGs categories can be defined as either basic or complex.
AB-CG has a set of basic categories that contains S (for sentences) and N (for
nouns). Complex categories, are composed of more than one category separated
by forward or backward slashes, which are operators over categories. Given that
X and Y are variables over categories, the directional slash operators can be
described as follows:
• the forward slash is used with rightward combining categories, represented
as X/Y, denoting that this category needs to combine with a category Y to
its right to yield X, and
• the backward slash operates over leftward combining categories, X\Y,
indicating that the category needs to combine with a category Y to its left
to yield X.
Complex categories can be seen as incomplete units: a category X/Y, for
example, needs an element of category Y to give as a result category X. In terms
of function applications category X/Y is a function from the argument Y (the
subcategorised category that is needed) to a complete expression X which is
known as the result or value. In this way, an adjective that has category N/N is
identified as a function from N (the argument) into N (the result), indicating that
it is a category which needs an N to form another N. Throughout this document,
the notation used specifies a complex category with the argument always to the
right of the slash and the result to the left.
56
The set of categories is the inductive closure of the set of basic categories
under the slash operators, such that it contains the basic categories and the
categories that can be defined using the slash operators. As categories can be
defined recursively, if X and Y are categories, X/Y and X\Y are also categories.
As a consequence, categories can have more than one argument and mix these two
kinds of slashes (e.g. (X\Y)/Z), being able to combine with different arguments
in different directions. However, in languages in general the number of arguments
of a complex category is small. For instance, for English the maximum number
seems to be five, for a small number of verbs such as bet (I bet you five pounds
for Red Rum to win [from Briscoe 1999]).
These categories are combined by means of the Functional Application
Rule. This rule simply combines a function with its argument. In this way, a
complex category that needs an argument is applied to an adjacent category that
is equal to the argument needed. This rule has two versions:
• the Forward Application rule allows a rightward-combining category
(X/Y) to combine with an argument (Y) to its right. This rule, which
in a derivation is represented as ‘>’, can be defined as:
X/Y Y → X
Figure 4.1 shows the use of the forward application rule to combine the adjective big, which has category N/N, with the noun dog, which has category
N.
Throughout this document, in a derivation, the combination of categories is
indicated by a solid line underlining the categories involved, ending with the
symbol of the rule used and with the resulting category written underneath.
• the Backward Application rule (<) is used to combine a leftward-combining
category (X\Y) with its argument (Y) to the left:
Y X\Y → X
Although AB-CG, with two atomic categories (S and N) and two rules (forward and backward application), can capture some linguistic constructions, it is
considered to be inadequate to handle natural languages even by its authors.
Figure 4.1: Using Forward Application
57
4.1.2
Extensions to AB-Categorial Grammar
Most of the work in the area extends AB-CG in terms of the basic categories
defined and/or in terms of the rules used. The basic category set is extended by
including categories like NP (for noun phrases) PP (for prepositional phrases),
VP (for verb phrases), ADJP (for adjectival phrases), ADVP (adverbial phrases),
among others. In relation to the set of rules, the following are some of the rules
that are used in different configurations of CGs.
The rule of Associativity (A) states that a function with two arguments,
one on either side, can combine with them in either order:
• (Y\X)/Z → (Y/Z)\X
• (Y/Z)\X → (Y\X)/Z
Associativity can be used to combine, for example, a transitive verb syntactically with either the object or the subject first, as can be seen in figures 4.2 and
4.3, in the derivations of the sentence John likes Mary. This rule guarantees that
the semantics of the verb is still intact, with the subject and the object being
assigned the correct roles in the semantics, even if the order in which they are
combined has changed.
John
NP
Figure 4.2: First
likes
Mary
(S\NP)/NP
NP
>
S\NP
<
S
likes
Mary
John
NP (S\NP)/NP
NP
>
Derivation ofS\NP
Sentence<John
S
John
Mary
likes
NP (S\NP)/NP A NP
(S/NP)\NP<
S/NP
John
Mary>
likes
S
NP (S\NP)/NP A NP
(S/NP)\NP<
S/NP
>
S
John
gave
Mary
NP
((S\NP)/NP)/NP
NP
likes Mary
a
Figure 4.3: Second Derivation of Sentence John likes Mary
<T
NP/N
flower
N
>
((S\NP)/NP)\(((S\NP)/NP)/NP)
NP
<T
John
gave
Mary
flower
a
The rule of Functional Composition allows a functor(S\NP)\((S\NP)/NP)
category missing
NP ((S\NP)/NP)/NP
NP
N<B
NP/N
>
an argument to compose with an adjacent function
that outputs
<T that argument
(S\NP)\(((S\NP)/NP)/NP)
((S\NP)/NP)\(((S\NP)/NP)/NP)
NP
<
as its result. For example, the word will is an auxiliary
verb with category
<T
S\NP
(S\NP)\((S\NP)/NP)
<
(S\NP)/(S\NP) and the word buy is a transitive verb with category
(S\NP)/NP.
<B
S
(S\NP)\(((S\NP)/NP)/NP)
<
58
S\NP
<
S
John
gave
Mary
a
NP
(S\NP)/(NP*NP)
NP
NP/N
John
gave
Mary
a
flower
NP
N
>
flower *
Thus will and buy can be combined by composition to form the constituent will
buy with category (S\NP)/NP. There are two versions of this rule:
• Forward Composition (>B) allows the combination of an item (X/Y)
with another item (Y/Z) to the right:
X/Y Y/Z → X/Z
This rule is used in the derivation of the sentence Mary will buy the car, as
shown in figure 4.4.
• Backward Composition (<B) allows the combination of the argument
of a complex category (X\Y) with the result of the category to its left (Y\Z):
Y\Z X\Y → X\Z
While application must absorb a complete constituent, composition is used
to combine contiguous strings that do not form what is traditionally known as a
constituent. In this way, it is possible to obtain items like will buy and Mary will
buy by composing their categories. CGs, unlike other formalisms, consider will
buy and Mary will buy genuine constituents because they form prosodic units
and they have a coherent semantics [Steedman 1990].
"!
#$
%
Figure 4.4: Using Forward Composition
Type Raising rules turn arguments into functions over functions over such
arguments. For example, given that S\NP is a function over argument NP,
through type raising the category NP becomes the category S/(S\NP), i.e. a
function (S/) over a function over NP (S\NP). By allowing arguments to turn
into functions, it is, then, possible to compose them with other functions. There
are two versions of this rule:
• Forward Type Raising (>T) allows the transformation of category X
into a higher order category function with the purpose of combining it with
59
a constituent to its right:
X → Y/(Y\X)
This rule is used to transform subjects from NPs into S/(S\NP). It is used
in the derivation of sentence Mary smells and I paint the flower, as shown
in figure 4.5.
• Backward Type Raising (<T) allows a category X to be raised into a
higher order category function in order to be combined with a constituent
to its left:
X → Y\(Y/X)
It is used to transform indirect objects into functions from ditransitive
verbs into transitive verbs and direct objects into functions from transitive
to intransitive verbs. This rule can be used to capture, among other constructions, coordinations such as the one in the sentence Jane shows Mary
the pictures and John the paintings, whose derivation is shown in figure 4.6.
- +
.
"!
#
- 0.
- 21
.
. $"% &
&'"
/.
( )+*,
21
3
.
Figure 4.5: Using Forward Type Raising
Raising extends the weak generative power of the grammar in the description
of non-standard constituent structures. Since raising is a recursive rule, an argument can be raised over its functor, which can be raised over the new category
of the original argument and so on ad infinitum. However, this recursion can be
restricted, for example, by constraining the raised categories to those defined in
the lexicon or by applying the rule only when there is no other way to obtain a
derivation.
The Division (D) rules are unary rules that are applied to both sides of the
main slash operator in a functor category:
• X/Y → (X/Z)/(Y/Z)
• X\Y→(Z\X)\(Z\Y)
60
-+%
"! #
$%
&(' )$*!%
+,
-"(+
/ $%
&' +$' +.(
Figure 4.6: Using Backward Type Raising and Backward Composition
Lambek [1958] used this rule to show that a sentence-modifying adverb is also
a predicate-modifying adverb: S\S → (S\NP)\(S\NP), being able to generate alternative analyses for the sentence Bill runs here, figures 4.7 and 4.8.
23 4 4
57698:
;=<
0
@AB5A
1 ;><
0
0
1 0
?
0
?
Figure 4.7: First Derivation of Sentence Bill runs here
IJ K K
F>G
L7M9NO
D
QRBLR
E F>G
D
C7D
D
E F>GH E C7D
D
E F>G
E D
E F>GH
P
S
S
Figure 4.8: Second Derivation of Sentence Bill runs here
Division preserves word order and logical implication, but, due to the fact that
it is recursive, it causes the extension of the power of the system to structural
completeness. This means that any substring can be a constituent and any item
in the substring can be its head [Wood 1993]. It leads to the extreme case
of spurious ambiguity, where different derivations are generated with the same
semantic interpretation.
The Backward Crossing Substitution is one of the Substitution rules and
it is used in the treatment of parasitic gaps such as the one in the sentence Mary
61
will copy and file without reading any articles longer than ten thousand words,
from Steedman [2000]:
• Backward Crossing Substitution (<Sx): Y/Z (X\Y)/Z → X/Z
The rule of Generalised Weak Permutation (GWP) [Briscoe 1997] rotates
the arguments of a complex category, allowing a functor category to combine with
its arguments in any order, while keeping the original direction associated with
each argument:
• Generalised Weak Permutation (P): ((X|Y1 ) . . . |Yn ) → (((X|Yn )|Y1 ) . . .)
where ‘|’ is a variable over ‘/’ and ‘\’. If the arguments of a complex category
are ordered in a way that does not allow the category to be combined, the GWP
rule rotates the arguments until they are in an appropriate order for combining
with an adjacent category. However, the number of possible permutation operations over a category is finite and bounded by the number of arguments of the
category in question. Thus, for example, a functor category with three arguments
has three different argument sequences, as can be seen in the case of an oblique
transitive verb like donates:
• ((S\NP1 )/PP)/NP2 ,
• ((S/NP2 )\NP1 )/PP and
• ((S/PP)/NP2 )\NP1
In practical terms the application of GWP can be controlled, for example, by
maintaining a count of the number of permutations performed with respect to
the possible permutations for a given category.
While the associativity rule is restricted to be applied to functor categories
with two arguments, the permutation rule can be applied to a functor category
with any number of arguments, which can be combined in any order.
Since GWP can generate all the different orderings of arguments for a given
complex category, this rule allows the grammar to capture more flexible constituent orders. For instance, the oblique transitive verb donate, whose initial
category is ((S\NP1 )/NP2 )/PP, captures not only sentences where the subcategorised constituents follow this initial ordering as in She donated to the school
those computers, but also the ones where the ordering is different as in She donated
those computers to the school. The derivations for these sentences are shown in
figures 4.9 and 4.10 respectively. As a consequence, there is no need to define
extra categories for capturing more flexible constituent orders if they differ in the
order in which constituents are combined, because these are already produced by
GWP. This rule is also used to capture, among other constructions, unbounded
62
&
%
! " $# " %&$ $&' % &
)
)
%
%
)
$
)
! " %$#(&' )
" %
*
Figure 4.9: Derivation of Sentence She donated to the school those computers
+,- . /012-.
2 ,/3- 4/57682-9:3 2 /
2',3 4,//;
<%= >?+ @ <%=$A(B<%=B=$= %
< =B<
<
<
=$= B'< = <%=B<
E
E
>?+CB=$=$A @ <%=B'< = D
<%=
<%=
E
E
>+CB=$=$A @ < =
$= =
F
+CB=$=
E
+
Figure 4.10: Derivation of Sentence She donated those computers to the school
dependencies, such as the one in the sentence Who does Goldie love?, which are
discussed in section 4.4.
Associativity, Composition, Division and GWP introduce so-called “spurious
ambiguity”, which is the property where alternative constituent structures for a
sentence have the same semantic interpretation. Figures 4.11 and 4.12 show
two alternative semantically equivalent derivations for the sentence Jane eats
the cake. Wood [1993] notes that in most cases spurious ambiguity will not
affect the grammaticality judgements for particular sentences. It rather causes
a processing problem, since for a given sentence, it allows many derivations to
be generated that have equivalent semantic interpretations. Steedman [1991]
also notes that the alternative derivations generated, far from being spurious,
are genuine ambiguities at the level of Information Structure. Moreover, as the
spurious ambiguity caused by these rules is not considered to be a problem in the
scope of this research, this issue is not going to be addressed here.
QLRJ
N%O
H'IJ
N%OPN
JLHS
TU V N%O$W(PN%O
U
U V N%O
N%O
KLMJ
N
G
GX
Figure 4.11: First Derivation of Sentence Jane eats the cake
63
!
Figure 4.12: Second Derivation of Sentence Jane eats the cake
The rules described in this section are some of those that can be used to
extend the basic AB-CGs. Apart from them, some proposals also extend the set
of operators used to build complex categories. In this case, besides the two slash
operators, a third one known as the product operator (∗) [Lambek 1958] can
be used. The product operator is used to form an ordered pair from two adjacent
categories. Thus a complex category that needs to combine with two arguments
(e.g. (X/Y)/Z), one at a time, by two operations of functional application can
combine with the product of these arguments (Z*Y) in a single operation. For
instance, the verb ‘gave’, with category ((S\NP)/NP)/NP, can also be assigned
the equivalent category (S\NP)/(NP*NP). Wood [1989] uses this equivalence to
capture coordinations such as the one in the sentence He gave Bill a guitar and
Helen a piano (figure 4.13).
<=2
-/.1032
45 6 6
.
-7/5 8.9
$%
"#, * $%)+"@$%'&($%)
$%
$%+$
$
$%
.:;
A
$%'&($%
<=2/6 2/:
"#"$%'&($%) * " $%'&($%))+"$%'&($%) $%
.
> 5 .:?
$%+$
$
$%
C
A
$%'&($%
"$%'&($%) * "$%'&($%)
C
A
B
$%'&($%
A
, * $%
B
,
Figure 4.13: Derivation of Sentence He gave Bill a guitar and Helen a piano
Another possible extension of the basic CGs is obtained by using combinators. Combinators “bear a striking resemblance to the ‘combinators’ which
Curry and Feys [1958] use to define the foundations of the lambda calculus and
all applicative systems - that is, systems expressing the operation of functional
application and abstraction’ [Steedman 1988]. The combinators used in Steedman’s Combinatory Categorial Grammars (CCGs) are three: B (functional
composition), T (type raising), and S (substitution).
1. B is the combinator for functional composition. Given the functions F
and G, the use of this combinator results in the composition of these two
64
functions, whose semantics is given by the following identity:
• BFG=λx F(Gx )
where F and G represent functions, and x and y represent their arguments.
Thus, the rule of Forward Composition can be rewritten as:
• X/Y:F Y/Z:G ⇒ X/Z: λx F(Gx )
indicating a category X/Y with interpretation F which is forward composed
with a category Y/Z with interpretation G, giving as a result a category
X/Z with interpretation BFG. Given the example in figure 4.4, the application of this rule to will and buy results in the appropriate interpretation:
λx.λy.will(buy(x,y))
2. T is the combinator for type raising, which is defined as:
• Tx =λF Fx .
A function of two arguments is mapped onto a function of one argument,
that identifies the two arguments.
3. S, the functional substitution combinator, has semantics defined according
to the following equivalence:
• SFG=λx Fx (Gx )
This rule allows a two-argument function (X\Y)/Z with interpretation F
to be combined with a one-argument function Y/Z with interpretation G,
yielding a function of category X/Z, which has interpretation SFG.
Steedman’s proposal of CCGs respects formal and linguistic considerations,
with these combinators being used to express, in a natural way, almost all rules
needed for natural language description.
It is also possible to define a CG as a unification-based grammar, where
objects are described in terms of attribute-value pairs. Using such an approach,
specific attributes can be defined, for example, to account for agreement. In this
case, the information related to number and person, for example, is specified in
the appropriate attributes and can be added to a category like N. Thus, a noun
like dogs has the value ‘plural’ for the number attribute and the value ‘third’ for
the person attribute. Furthermore, attributes can have variables as values. For
example, in the case of a determiner like the, which can be used with singular
as well as with plural words, the value for the number attribute is a variable,
allowing it to be used with both singular and plural words. Different ways of
65













W : walks

C : s[fin]/np[nom]:x:pre 


S : [e]walk(e,x)

O :
Figure 4.14: UCG’s Encoding of walks






















CAT : s




FORM : finite



DIR : left





 CAT : np




ARG :  AGR :  PERS : 3   

NUM : sg  
VAL
: 

Figure 4.15: CUG’s Encoding of runs
combining the principles of CGs and those of unification-based formalisms were
proposed. In what follows, some of these proposals are briefly discussed.
Unification
Categorial
Grammar
(UCG)
[Zeevat et al 1987],
[Zeevat 1988] is a proposal of a CG enriched by some aspects of unification. In UCG, a verb such as walks is encoded as shown in figure 4.14
where:
• W specifies that the orthography of the word is walks,
• C that it is an intransitive verb which needs an argument NP in the nominative case preceding the verb (pre) to form a finite sentence (s[fin]), and
the NP has its semantics represented by the variable ‘x’,
• S specifies its semantics, and
• O is left unspecified.
In CCGs, Steedman [1996] regards the basic categories like S and NP as
complex objects that include the use of attribute-value pairs. Thus, a third
person singular word such as loves is represented as (S\NP3s )/NP, where NP3s
specifies that the subject should be a third person singular NP. However, he does
not discuss the attributes used or how they should be encoded in the categories.
Categorial Unification Grammar (CUG) [Uszkoreit 1986] encodes the
essential properties of both formalisms: unification and Categorial Grammars.
CUG describes an intransitive verb such as runs as shown in figure 4.15, where
VAL describes the functor, DIR gives the direction of the argument and ARG
has the specifications of the argument.
66
The advantage is that CUG is a general framework, while UCG is a specific individual theory of CG that adopts some insights from unification-based
formalisms. As a consequence UCG is not as general as CUG.
These are some of the possible extensions to the basic AB-CG that have been
proposed. Different versions of CG use these extensions in different configurations. For example, Lambek Calculus [Lambek 1958] uses the rules of application, composition, associativity, raising and division, and the product operator. 1
Steedman’s CCG [Steedman 1988 to 2000] includes S, N, NP, PP and CONJ in
the category set and uses the combinators and the rules of application, composition, type raising, substitution and coordination. Hoffman [1995] uses multi-sets
CCGs to define a system that is able to handle scrambling elegantly, capturing
languages with freer word order than English, like Turkish. CCGs are also used
by Doran and Srinivas [1998] and Hockenmaier et al. [2000] as wide-coverage
grammars.
4.2
UB-GCGs
Unification-Based Generalised Categorial Grammars (UB-GCGs), the
particular version of CG used in this work, extend basic CGs, by defining the
basic categories in terms of bundles of attribute-value pairs, as in CUG, and by
using an extended set of operators and rules, also in terms of attribute-value pairs:
directional slashes and the product operator, the rules of application, composition
and generalised weak permutation. There are five basic categories: S (sentence),
N (noun), NP (noun phrase), PRT (particle) and PP (prepositional phrase);
other categories are defined in terms of these. This particular configuration of
CG was chosen because it could successfully capture the constructions found in
the corpus, as discussed in section 4.6, without adding unnecessary descriptive
power.2
The UB-GCG implemented follows the sign-based approach to linguistic analysis [Pollard and Sag 1987], where words and categories are represented in terms
of TDFSs, with different kinds of linguistic information being simultaneously
represented as a conjunction of attribute-value pairs that form a sign. A sign is
composed of three attributes (figure 4.16):
• orth encodes the orthographic description of words,
• cat encodes syntactic aspects related to the categories, and
• sem encodes the semantics associated with a particular word.
1
For an extensive description of the Lambek Calculus see [Moortgat 1988].
The descriptive power of a very similar system is investigated by Hoffman [1995], and
she demonstrates that such system is able to successfully handle long-distance scrambling,
generating some mildly context-sensitive languages.
2
67







sign

ORTH : diff-list 

CAT : cat

SEM : sem

Figure 4.16: Sign
Figure 4.17: A Type Hierarchy
The values that these attributes take correspond to types in a hierarchy.
Figure 4.17 shows a small fragment of the complete hierarchy. An attribute
specified as taking a type as value can also take any of its subtypes as valid
values. This is shown in figures 4.16, for the general description of a sign, and
4.18, for the more specific description of a noun phrase sign. In these FSs np is
a subtype of cat in the hierarchy defined in figure 4.17.
In the next sections, the theories used to encode the syntactic, semantic and
linking information in the grammar are presented.
4.2.1
Syntax
The syntactic properties of signs are formalised in the attribute cat. Categories
are divided in terms of valence, depending on whether they are saturated or
unsaturated. Atomic categories are saturated which means that they do not
subcategorise for any other categories [Wood 1993]. The categories in the set of
basic categories are saturated: S, NP, N, PP and PRT. They are distinguished
in terms of appropriate feature instantiation, as shown for the NP sign in figure
4.18.
Complex categories are unsaturated, subcategorising for other categories. For
instance, an intransitive verb subcategorises for an NP subject to the left and
results in an S category, with its category being S\NP, while a preposition sub






np-sign

ORTH : diff-list 

CAT : np

SEM : sem

Figure 4.18: NP sign
68
























complex-cat
RESULT:SIGN
: sign

diff-list




list


ACTIVE




: 







LST



: 




HD



SIGN : sign
DIRECTION:DIR-VALUE
list

: 

TL :
LAST : list
:
direction
































Figure 4.19: Complex Category Type
categorises for an NP to the right, to form a PP, with category PP/NP. In terms
of feature structures, complex categories are recursively defined in terms of two
attributes following Steedman [1988]:
• result describes the functor category, and
• active describes the list of subcategorised argument categories,
both defined in cat. result has one attribute, sign (with orth, cat and sem),
which is instantiated according to the particular result category. active encodes
the subcategorisation list of the category, where each of the subcategorised categories has two attributes: sign and direction, figure 4.19. The attribute
direction encodes the direction in which the category is to be combined, where
dir-value can be forward or backward, corresponding to the forward and
backward slash operators, respectively. The categories defined in result and in
active can be either atomic or complex themselves. As an example, an intransitive verb (S\NP) is encoded as shown in figure 4.20. The active attribute is
implemented as a difference list, with attributes lst (list) and last (last). Both
can have as value a list, which can be either a non-empty list with head (hd) and
tail (tl), or an empty-list with value e-list. In a non-empty list the head takes
any valid value, and the tail takes a list which can be either empty or non-empty.
A difference list is a special structure that maintains a pointer to the end of the
list, with the last tl element in lst being coindexed with last (figure 4.20).
In unification-based encoding, in general, difference lists are used as a way of
appending lists using only unification [Copestake 2002]. Figure 4.20 shows the
encoding of an intransitive verb whose only argument is defined in lst:hd. It
has the last attribute specified by default as e-list, marking the end of the list,
and coindexed with lst:tl. This notation for difference lists can be represented
in an abbreviated form where ‘<!’ marks the beginning of the list (lst:hd) and
‘!>’ marks the end of the list (last), and the elements in the subcategorisation
list are separated by commas (figures 4.21 and 4.22).
This notation for CGs is based on the one used by Steedman [1991a], which
was modified to allow a concise implementation of a default inheritance hierarchy
69
























intrans
RESULT:SIGN:CAT
: s

 diff-list



list



ACTIVE



: 







LST



: 




LAST
HD
TL



: 

: /

SIGN:CAT : np
DIRECTION:DIR-VALUE
1 e-list
:
backward
: / 1
































Figure 4.20: Intransitive Verb Type








intrans
RESULT:SIGN:CAT
: s

SIGN:CAT
: np

ACTIVE : <!
DIRECTION:DIR-VALUE

:
backward





/! > 


Figure 4.21: Intransitive Verb Type Abbreviated
of types, where information is defined only once and propagated through the
hierarchy. In Steedman’s notation, a complex category is defined as a nested
structure, as can be seen in figures 4.23 and 4.24 for intransitive verbs and
transitive verbs, respectively. On the other hand, in this work a complex category
is defined as a list of sequentially defined subcategorised elements, with each
element encoding not only the sign, but also the direction attribute. In terms
of the inheritance hierarchy, this means that a given subtype inherits the active
list from its supertype. If the subtype subcategorises for more categories, these
are added in the end of the list, overriding the inherited default end of the list
(/ ! >). This can be seen in figure 4.22 that shows trans, which is a subtype
of intrans, encoding transitive verbs. In this figure, the first subcategorised
element in the active list is the most general type > which can represent any
category. Trans is expanded as shown in figure 4.25, having all the information
contained in intrans, where > is unified with the first subcategorised element in
intrans, the NP subject. Trans also adds to the end of the active list another
NP category, with direction forward, and a default end of the list (/! >).
These defaults are only used for encoding generalisations and are transformed
into indefeasible information using the DefFill operation. DefFill can be used,
for example, at the interface with the lexicon, so that, unless otherwise required,
lexical entries have only non-default information. For instance, a transitive verb
has the default specifications in trans changed to non-default (figure 4.26), where
the end of the list is made indefeasible.
70






trans
ACTIVE
: <!
>

,
SIGN:CAT : np
DIRECTION:DIR-VALUE
:
forward




/! > 


Figure 4.22: Transitive Verb Type







intrans

RESULT:SIGN:CAT : s 
DIRECTION : backward 
ACTIVE:SIGN:CAT : np

Figure 4.23: Traditional Encoding for Intransitive Verbs














trans

RESULT:SIGN:CAT : s
DIRECTION : backward
ACTIVE:SIGN:CAT : np
DIRECTION : forward
ACTIVE:SIGN:CAT : np
RESULT


: 















Figure 4.24: Traditional Encoding for Transitive Verbs
4.2.2
Semantics
The semantic properties of words are represented using a neo-Davidsonian
style event-based approach to semantics [Parsons 1980] [Sanfilippo 1990],
[Copestake et al. 1998], [Sag and Wasow 1999]. It is based on the approach
developed by Davidson [1967], where the basic idea is that propositions involve
explicit reference to events. Davidson proposed that events should be treated
as primitive ontological elements and should be explicitly defined in the logical
form of verbs expressing actions, with such verbs including an argument place
for event terms. For example, in the logical form of the sentence Fido chases
the cat in the park the event term ‘e’ is an argument of both the verbal and the
prepositional predicates:
λe.chase(e,Fido,the(cat)) ∧ in(e,the(park))
Such an approach provides a natural account of the entailment relation between sentences. For example, the sentences 4.1 and 4.2 differ only in terms of
the modifier in the park.
• (4.1) Fido chases the cat in the park
• (4.2) Fido chases the cat
The first sentence entails the second: if the first sentence is true (that Fido
71















trans


RESULT:SIGN:CAT
: s


 


SIGN:CAT
:
np
, 
ACTIVE : <!
DIRECTION:DIR-VALUE : backward 





/! >
 SIGN:CAT : np

DIRECTION:DIR-VALUE : forward

Figure 4.25: Transitive Verb Type Expanded















trans


RESULT:SIGN:CAT
: s


 


SIGN:CAT
: np


ACTIVE : <!
,
DIRECTION:DIR-VALUE : backward 





 SIGN:CAT : np
! >

DIRECTION:DIR-VALUE : forward

Figure 4.26: Transitive Verb Type Expanded and DefFilled
is chasing the cat in the park), then the second one (that Fido is chasing) is
also true, but the converse does not hold. This is reflected in their logical forms,
respectively:
• λe.chase(e,Fido,the(cat)) ∧ in(e,the(park))
• λe.chase(e,Fido,the(cat))
In this work a neo-Davidsonian style semantics is implemented in terms of a
variant approach of Minimal Recursion Semantics (MRS) [Copestake et al. 1998].
MRS is characterised as being a flat semantic framework that does not use embedded structures, with the elements within a flat representation being relations.
To simulate recursive embedding, MRS uses identifiers, which are unified with
the role arguments of other relations. However, unlike other approaches to flat
semantics, MRS provides a treatment of standard quantification. Moreover, MRS
can be easily integrated in a feature-based grammar.
The MRS variant implemented in this work follows Sag and Wasow’s version
[Sag and Wasow 1999] which is a simplification of the MRS defined by Copestake
et al. [1998]. Although the grammar implemented uses this simplified version, it
could be easily extended to a complete MRS account. In Sag and Wasow’s version,
semantic objects are implemented as TDFSs describing events or situations (sit),
e.g., a running event in Bill is running. Each of these events is classified in relation
to its semantic mode (mode) as:
• propositions (prop),
• questions (quest), or
72
• directives (dir).
Besides the semantic mode, two other attributes are also used to describe semantic objects: an index (index), which corresponds to the event or individual
referred to, and a restriction (restr), which specifies the list of conditions that
has to be fulfilled for the semantic expression to be applicable. index can take
one of three values, according to the object it is referring to: index, corresponding to situations, null-index, corresponding to a null object and imp-index
corresponding to the implicit subject of an imperative sentence. The conditions
associated with individuals and situations that have to be satisfied for the expression to hold are described by restr. Figure 4.27 shows the specification of the
general semantic type. These restrictions are described in terms of predications,
which provide a general way of specifying relations among semantic objects. A
predication specifies what kind of relation is involved and which objects are taking
part in it, as shown in figure 4.28 for a love relation. Verbs have attributes representing the actor or agent role (e.g. lover) and the undergoer or patient role
(e.g. loved). A more general nomenclature for semantic roles is being adopted
in this thesis, but it is compatible with and can be easily mapped to that defined
by Davis [1996] or Sag and Wasow [1999]. Thus, for instance, lover is mapped
to arg1 and loved to arg2. As a consequence, the predication in figure 4.28
is generalisable to the one in figure 4.29.







sem

MODE : mode 
INDEX : index 
RESTR : diff-list

Figure 4.27: Semantic Type










restr


RELN : love



SIT : index

LOVER : index 
LOVED : index

Figure 4.28: Sample Predication in restr
The role arguments within predications are represented in the attributes arg1
to argn. An element with predication semantics, such as a verb, specifies links
between the indices of the role arguments in its predication and the other semantic
predicates on the restr list. This can be seen in figure 4.30, which shows the
semantics for the verb love in the sentence Bill loves Mary. In this figure, the love
predicate specifies that arg1 (the lover role) is coindexed with the predicate
representing Bill, with tag 1 , while arg2 (the loved role) is coindexed with
the predicate representing Mary, with tag 2 .
73










restr

RELN : love 
SIT : index 
ARG1 : index 
ARG2 : index

Figure 4.29: Equivalent Sample Predication restr
















sem


MODE : prop



INDEX : 0  index




 


RELN
: love





  SIT : 3 index   SIT : 4 index 

 SIT : 0
 
 

RESTR : <!
,  NAME : Bill
,  NAME : Mary ! > 

 
 

ARG1
:
1
index




NAMED
: 2
NAMED
: 1
ARG2 : 2 index

Figure 4.30: Logical Form of the sentence Bill loves Mary
The construction of the restr list for a sentence adopts the Compositionality
Principle, which states that the meaning of a constituent is composed of the
meaning of its parts. Thus, in a derivation, the resulting restr value (figure
4.30) is the sum of the restr values of the combined categories, with each word
in the sentence being assigned an appropriate semantic value.
4.2.3
Linking
Linking theories try to capture regularities in the mapping between the semantic
argument structure and the syntactic subcategorisation frame of a predicator.
For instance, the agent role in an action denoted by a verb is usually realised as
the subject of the verb, as in The dog chases the cat where the verb’s subject, the
dog, is the agent role of the chasing action, while the cat is the affected patient
role of the action and is realised as the verb’s direct object. The linking generalisations adopted in the grammar are represented as constraints in an inheritance
hierarchy, following the approaches defined by Wechsler [1995] and Davis [1996].
The specified linking types encode constraints between semantic roles and syntactic arguments, with each linking type partly defining the mapping between
them. The constraints associated with linking types specify the semantics of the
predicators they apply to, and the various constraints that apply to a given type
combine to determine, at least partly, its subcategorisation frame. On the other
hand, subcategorisation is not considered to be completely semantically driven,
being partly arbitrary, as in the case of semantic roles that are optionally realised
syntactically. Thus it is also necessary to specify some subcategorisation information in the linking types, taking into account the notion that subcategorisation
can be partly independent of semantics. In this way, it is the combination of
the independent specifications of a predicate semantic arguments and syntactic
74
subcategorisation frame that determine the predicate’s linking pattern.
Wechsler’s HPSG formulation of linking constraints uses four different structures to encode and link the relevant mapping between semantic and syntactic
arguments. On the syntactic side, subcategorisation frames are defined in two
attributes: subj, containing the subject, and comps, containing the other complements. These two attributes are the locus of phrase structure concatenation, as
determined by the Valence Principle [Pollard and Sag 1994]. Another attribute,
roles, contains the union of the subj and comps lists. This list is the locus of
lexicosemantic generalisations about argument structure. content contains the
appropriate argument structure. For example, the verb love is defined as shown
in figure 4.31.














SUBJ : <NP[nom]>



COMPS : <NP>


ROLES : <NP[nom],NP>





REL
:
love


CONTENT :  LOVER : index  
LOVED : index

Figure 4.31: Lexical Description of love
The Linking Principle as defined by Wechsler specifies that:
• the subj list item is reentrant with the leftmost syntactically possible roles
list item (for English, NPs or complementiser-introduced clauses);
• the comps list contains any remaining roles list items.
The ordered elements in roles are mapped to the semantic arguments in the
content attributes. These constraints are specified as follows, with the semantic
arguments in content generically specified as arg1 to argn:



















SUBJ : < 1 >
COMPS : < 2
ROLES : < 1
CONTENT

... n >
3





: 



, 2
4
, ...




n m >










3






4






m
REL : rel
ARG1 :
ARG2 :
: ...
ARGN
:
Figure 4.32: The Linking Principle
When this principle is applied to a lexical sign like love, the sign shown in
figure 4.33 is produced.
This HPSG formulation has to be translated to the UB-GCG equivalent,
where the subj and comps lists are combined together in the cat:active list,
75















SUBJ : < 1 NP[nom]>
COMPS : < 2 NP>
ROLES : < 1 3 , 2 4 >

 REL : love
CONTENT :  LOVER : 3
LOVED : 4




















Figure 4.33: Linking Principle Applied to love - HPSG Formulation










CAT:ACTIVE
SEM:RESTR
:
SIGN : 1 NP
 REL : love 


 ARG1 : 1 


ARG2 : 2
: <!

,
SIGN
:
2
NP

!>








Figure 4.34: Linking Principle Applied to love - UB-GCG Formulation
roles is non-existent, and content corresponds to sem:restr, as shown in
figure 4.34. The basic difference between these two formulations is that the
HPSG version encodes separately the subject, in subj, and the other verbal
complements, in comps, and they are ordered for linking according to the roles
they perform in roles. The UB-GCG formulation specifies all these aspects
directly in cat:active, where each subcategorised element is ordered and is
directly linked to its role in sem:restr.
The formalisation of the linking theory adopted follows Davis’ [1996] use of
inheritance hierarchies to define linking relations. In this way, linking generalisations can be encoded in types higher up the hierarchy to be propagated
throughout the network. As a consequence, the linking constraints defined in a
given type are inherited by its subtypes which can also add extra constraints,
making effective use of the inheritance mechanism.
4.2.4
The Grammar
The UB-GCG is implemented as a default inheritance network of types in order to
structure the linguistic information defined and reduce the problem of redundancy
in lexical specification [Villavicencio 1999], [Villavicencio 2000b]. The network of
types is implemented using yadu, the symmetric default unification operation
described in section 3.6, with different hierarchies defined for different levels of
description. The main hierarchies are for syntax, semantics, linking, and for
their combination in the resulting signs. The constraints on the types are defined
in terms of TDFSs, which contain only the appropriate attributes associated
with a particular type. The mechanisms of grammar implementation discussed
in chapter 3 are all employed in the construction of this grammar and their
application is discussed in the following sections. Even though these mechanisms
76






basic-cat

CAT-TYPE : cat-type 
M-FEATS : m-feats
Figure 4.35: Basic Category



















CAT-TYPE : s-cat




 sent-m-feats



 VFORM : vform





 INV : boolean


M-FEATS :  AUX : boolean



 COMP-FORM : comp-form  




 TAKE-PARTICLE : boolean  


PARTICLE : string

Figure 4.36: S Category
have been successfully used in the description of several linguistic phenomena,
the discussion in this section concentrates on their application to structure the
lexicon. In the next sections, the main hierarchies are described, focusing mostly
on the verbal hierarchy which is rich enough to illustrate the advantages of the
approach chosen.
Syntactic Hierarchy
The syntactic dimension of the grammar is described using the attribute cat
in the types associated with the different parts-of-speech. As S (sentence), NP
(noun phrase), N (noun), PRT (particle) and PP (prepositional phrase) are the
basic categories, as defined in section 4.2.1, the other categories are defined in
terms of these. The basic categories are distinguished in terms of the values of
their attributes cat-type that encodes the category type, and m-feats that
encodes morphosyntactic information (figure 4.35). The attribute m-feats can
be further specified to reflect the particular characteristics of each of the basic
categories: sent-m-feats for the verbal categories (S), nominal-m-feats for
the other categories (N, NP, PRT and PP).
S categories need to encode aspects such as the particular form (vform) of a
verb (e.g. base, past, and so on), if the verb is an auxiliary (aux), if it is in the
inverted or canonical form (inv) and so forth (figure 4.36).
The other categories encode information about agreement (agr) and case
(case), among other aspects. By default a nominal category is defined as having
third person singular agreement (agr:/3sg), being countable (count:/true),
not being a pronoun (pron:/false), not being a locative word (loc:/false) or
a wh-word (wh:/false) (figure 4.37). These defaults are overridden by more
specific information or by lexical rules. cat-type and m-feats also indicate
whether the sign corresponds to:
77


































CAT-TYPE : np-cat




 nominal-m-feats



 PRON : boolean/false





 WH : boolean/false





 LOC : boolean/false





 P-FORM : string




M-FEATS :  CASE : case





 COUNT : boolean/true






agr








 PERSON : person/3






 AGR : 








 NUMBER : number/sg  



GENDER : gender
Figure 4.37: NP Category























CAT-TYPE : prt-cat




 nominal-m-feats


 PRON : boolean/false  





 WH : boolean/false





 LOC : boolean/false
M-FEATS : 




 P-FORM : string



 CASE : prt-case





 COUNT : boolean


AGR : agr

Figure 4.38: PRT Category
• a regular noun (e.g. apple, in He ate the apple, where cat-type:n-cat and
case:reg-case),
• a noun phrase (e.g. Bill, in Bill runs, where cat-type:np-cat and case:regcase),
• an oblique prepositional phrase argument of a verb (e.g. to Mary, in Bill
talks to Mary, where cat-type:p-cat and case:p-case), or
• a particle (figure 4.38) attached to a verb (e.g. up in Jane warmed up the
milk, where cat-type:prt-cat and case:prt-case).
This approach follows Sanfilippo [1993] and Carpenter [1998]. Thus, Ns, NPs,
PPs and PRTs are distinguished in terms of the value of the attributes cat-type
and case. For regular nouns and noun phrases, the case can be further specified
as being accusative or nominative, as appropriate. For both prepositional phrases
(PPs) and particles (PRTs), it is important to define the specific preposition or
particle form being used and this is done in the p-form attribute (e.g. p-form:to
in Bill talks to Mary).
For reasons of clarity, throughout this document only the relevant attributes
are shown, with the morphological attributes of the basic categories being omit78
saturated
unsaturated
ted, unless necessary. Regular
are represented as Ns, noun-phrases as NPs,
commonnouns
unsaturated-non-nom
oblique argument prepositional phrases as PPs andtrans
particles as PRTs.
intrans-control
strict-intrans
Complex categories subcategorise for other categories, which are specified in
strict-trans
trans-control
intrans-raising
the active list. In the syntactic
hierarchy,
types defining
complex categories are
ditrans
trans-equi and number of the
ordered according to thewalkresult intrans-equi
constituent
and the category
trans-raising
subcategorisation argumentsseem
they specify.
like A fragment of the syntactic dimension
persuade
try
of the verbal hierarchy, which is based ongive
the sketch by Pollard and Sag [1987],
believe
is shown in figure 4.39.
intrans-control
intrans-raising
trans
seem
trans-control
try
intrans-control
walk
ditrans
intrans-equi
like
give
believe
persuade
subject-control
ask
promise
In the verbal hierarchy the subcategorised elements in the active list are ordered according to obliqueness [Dowty 1982], where subjects are the least oblique,
objects are the next most oblique, followed by indirect objects and finally by
oblique objects. The basic category, intrans, corresponds to the one assigned to
intransitive verbs (S\NP), figure 4.21, repeated in figure 4.40. It specifies the
need for exactly one subcategorised argument, the NP subject. The last element
of the subcategorisation list is, by default, ‘! >’, which marks the end of the
active list.
In terms of morphosyntactic attributes, verbs are defined as being by default in the base form (vform:/base), non-inverted (inv:/false) main verbs
(aux:/false), figure 4.40. These defaults can latter be overridden by more specific information or by lexical rules. For instance, auxiliary verb signs override the
default aux:/false with value true. All other syntactic verbal types are defined
as subtypes of intrans, representing the generalisation that all verbs subcategorise for at least an NP category. All the attributes specified in intrans, such as
that the NP should be in the nominative case, are inherited by instances of this
type and by its subtypes3 : for example, trans for transitive verbs, and intransIn this work the coverage condition, or closed world assumption [Carpenter 1992], which
79
ditrans
seem
try
trans-r
super-equi
Figure 4.39: The Proposed Hierarchy
3
intrans-raising
intrans-equi
trans-equi
trans-raising
int
common
intrans
give
believe
pe






















intrans
























/! > 
CAT-TYPE : s-cat
 sent-m-feats

RESULT:SIGN:CAT
M-FEATS :  VFORM : /base
 INV : /false

AUX : /false

ACTIVE : <! SIGN:CAT : np
DIRECTION:DIR-VALUE : backward






: 





Figure 4.40: Intransitive Verb Type






trans
ACTIVE
: <!
>

,
SIGN:CAT : np
DIRECTION:DIR-VALUE
:
forward




/! > 


Figure 4.41: Transitive Verb Type
control for intransitive control verbs, among others. However, since these types
subcategorise for 2 arguments, they need to override the inherited default end of
the list (/! >) and specify the addition of an extra complement: trans specifies
an extra NP complement ((S\NP)/NP) (figure 4.22 repeated here in figure 4.41),
and intrans-control an extra (S\NP) complement ((S\NP)/(S\NP)). Furthermore, each of these types also specifies the default end of the list (/! >), signalling
that these categories subcategorise by default for exactly 2 elements.
Similarly, the instances and subtypes of trans-control, which is a subtype
of trans (figure 4.39), inherit the default information that the predicative complement is controlled by the object. This is the case of the subtype trans-equi
(figure 4.42), for transitive-equi verbs, exemplified in sentence 4.3 with the verb
persuade. In this sentence, Mary is the object of persuade and is also the subject
of help (Bill persuaded Mary that she should help John).
• (4.3) Bill persuaded Mary to help John
Nevertheless, one of the subtypes of trans-equi, the type subject-control
for subject control verbs (figure 4.43) differs from the general case. For subject
control verbs, it is the subject of the transitive verb that controls the predicative
complement. Sentence 4.4 shows an example of the subject-control verb promise.
• (4.4) Bill promised Mary to help John
In this case, Bill, the subject of promise, is also the subject of help (Bill
promised Mary that he will help John). This behaviour is captured with the use
states that any type in a hierarchy has to be resolvable to a most specific type, is not used.
80





























trans-equi


RESULT:SIGN:CAT
: s






,

ACTIVE : <! SIGN : np-sign

DIRECTION:DIR-VALUE : backward






1
np-sign
SIGN
:
/

,



DIRECTION:DIR-VALUE
: forward








intrans-sign















RESULT:SIGN:CAT
:
s
 SIGN:CAT : 




/! > 




ACTIVE
: <! SIGN : / 1
!>









DIRECTION:DIR-VALUE : forward

Figure 4.42: Transitive Equi Verb Type Partially Expanded














subject-control
ACTIVE : <! SIGN







:
,
2
SIGN:CAT
:


np-sign SIGN : / 1 np-sign ,  






 intrans-sign




 /! > 
 ACTIVE : <!

!
>
SIGN
: 2 / 1





2 6↔ 1


Figure 4.43: Subject-Control Verb Type
of inequalities, which negate the inherited coindexation between the object of the
control verb and the subject of the predicative complement allowing the coindexation between the two subjects to hold (figure 4.43). This is a straightforward
encoding that allows for the definition of this type as a subtype of trans-equi
and which captures the common characteristics displayed by these types. The
possibility of using defaults and inequalities allows the capture of these generalisations, while avoiding a considerable amount of redundancy that would be
present in an alternative encoding. For instance, encoding subject-control as
a subtype of trans would require it to contain most of the information already
encoded in trans-control and trans-equi. It would also lose the generalisation
that all these types are closely related, where subject-control is a subregularity
of the general case.















trans


RESULT:SIGN:CAT
: s


 


SIGN:CAT
: np


ACTIVE : <!
,
DIRECTION:DIR-VALUE : backward 





 SIGN:CAT : np
! >

DIRECTION:DIR-VALUE : forward

Figure 4.44: Transitive Verb Type Expanded and DefFilled
81












super-equi ACTIVE : <! SIGN
,



np-sign SIGN : /p 1 np-sign ,  






 intrans-sign






 SIGN:CAT : 
/! > 


ACTIVE : < SIGN : /p 1 >  

:
Figure 4.45: Super-Equi Verb Type
The defaults just discussed are used to capture lexical generalisations, but
outside the lexicon we want them to act as indefeasible constraints. Therefore,
we use DefFill to make these default specifications indefeasible, except where
marked as persistently default. Thus, after DefFill, a type like trans has the
consistent default specification of the end of the list (/! >) incorporated and
specifies indefeasibly the need for exactly two arguments (figure 4.44). However,
this is not the case for the type super-equi, for super-equi verbs that accept
both object control or subject control, as is extensively discussed by Pollard and
Sag [1994, p. 308-317]. Sentence 4.5 shows the verb ask in a context where the
object of ask, Bill, is also the subject of go with object-control. In sentence 4.6,
it is the subject of ask (Mary) that is the subject of go, with subject-control. For
this type the information inherited from trans-equi, specifying default objectcontrol, is allowed to persist until discourse interpretation, using the p operator
(figure 4.45). Then, the default will survive if there is no conflicting information,
as in sentence 4.5, otherwise it will be overridden, e.g. if it occurs in the context
of sentence 4.6.
• (4.5) Mary asked Bill to go home. His mother was expecting him there.
• (4.6) Mary asked Bill to be allowed to go home. She was expected there.
This results in a direct encoding of such a phenomenon, without the need for
extra types being defined to allow for the alternative behaviour.
In comparison with Pollard and Sag’s hierarchy, shown in figure 3.1, repeated
in figure 4.46, the implemented encoding is much more compact. The syntactic
hierarchy defined has no need for types like strict-trans, which in Pollard and
Sag’s hierarchy is a subtype of trans and encodes exactly the same information.
The only difference between these two types is that trans works as an intermediate type, specifying at least two arguments (< np, np... >) and offering its
subtypes the possibility of adding extra arguments, as is the case for ditrans and
trans-control. At the same time, strict-trans specifies the subcategorisation
list as containing exactly two arguments (< np, np >), which is appropriate for
transitive verbs. Defaults automatically provide this possibility, by defining the
end of the list as default (/! >), avoiding the need for these redundant types.
In this way, while a hierarchy like Pollard and Sag’s is defined using 23 nodes,
a similar fragment of the implemented verbal hierarchy is defined using only 19
82
BC( $ D! "$ ! %
>[email protected]
H 19
E;F
"IB(
B! =J4
C"! E
G3G3
! ! ! " ! #
! " #$
! ! ! %
! #
&'!
! " 'D! $ ! K
"#$
! ! ! %
&('!
*)+*0
JL
4M/;22L
, 1 -32, 0
2* 4M2/
L2*/
)+*, -
9N<8.
8229
./0
, 1 -32
451 62
72, 1 262
:+2/;8<*=2
Figure 4.46: Pollard and Sag’s Hierarchy
nodes. This is a small fragment of the complete hierarchy, but it already shows
the advantages of using defaults. This hierarchy eliminates redundant specifications, like the strict-trans type, which are needed in a monotonic encoding.
By avoiding this redundancy, there is a real gain in conciseness, with the resulting hierarchy capturing linguistic regularities and sub-regularities, such as the
super-equi and subject-control types, in a compact encoding.
Semantic Hierarchy
The semantic representation used in the grammar is a variant of the MRS, as
presented in section 4.2.2, encoded in the attribute sem (figure 4.47).







sem

MODE : mode 
INDEX : index 
RESTR : diff-list

Figure 4.47: Semantic Type
The predication types in the semantic hierarchy are defined according to their
predicate-argument structure and organised according to the number of arguments they take. This information is encoded in the restr attribute of the
83
one-arg-sem
two-arg-sem
three-arg-sem
Figure 4.48: Fragment of the Verbal Semantic Hierarchy
semantics for a given verbal type. Figure 4.48 shows a fragment of the verbal
semantic hierarchy. The basic type in the verbal hierarchy is the one-arg-sem
(figure 4.49), which encodes generalisations about verbal categories:
• verb predicates have at least one argument (arg1), and
gendir
• by default the semantic mode corresponds to a proposition (mode:/prop).
subjdir
ndir2 vargdir
This is the semantic type associated with, for instance, intransitive verbs and
detdir
ndir
intransitive-raising verbs.4

one-arg-sem


MODE : /prop



INDEX : index




intrans-sign verb-pred









 RELN : reln
RESTR : <!
! > 




 SIT : index

ARG1 : index
trans-sign oblique-intrans-sign
intrans-equi-sign

intrans-raising-sign
oblique-trans-sign















Figure 4.49: One-arg-verb Semantics
ditrans-sign






trans-raising-sign
trans-equi-sign

two-arg-sem





verb-pred


RESTR : <!
!>

ARG2 : index
Figure 4.50: Two-arg-verb Semantics
The subtypes of one-arg-sem inherit this information, as can be seen in
the semantic verbal hierarchy (figure 4.48), while also defining extra arguments.
Thus, two-arg-sem shown in figure 4.50 requires an extra argument (arg2)
4
The type one-arg-sem contains a very general description and can be generalised to other
categories, such as adjectives, which also have only one semantic argument. This and some
other of the ideas presented in this chapter can be successfully achieved in principle, even
though the implemented grammar does not fully represent them as described.
84
one-arg-verb-linking
two-arg-verb-linking
one-arg-raising-verb-linking
three-arg-verb-linking
Figure 4.51: Fragment of the Verbal Linking Hierarchy
and it is the appropriate type for transitive verbs and intransitive equi verbs,
among others.
By defining the different semantic types using hierarchies, semantic information is propagated effectively from type to type, in an economic encoding of
semantic generalisations.
Linking Hierarchy
one-arg-sem
The mapping between syntactic subcategorised elements and semantic arguments
two-arg-sem
is defined in the linking
hierarchy. It is based on Wechsler’s [Wechsler 1995] and
Davis’ [Davis 1996] proposals, as explained in section 4.2.3. The linking theory
is implemented using three-arg-sem
coindexations between the syntactic attributes in cat and
the semantic attributes in sem.
Given that the subcategorised elements in the active list are ordered according to their obliqueness, the basic type in the linking hierarchy (figure 4.51) is the
one-arg-verb-linking type. It encodes the generalisation specified by the Linking Principle that, for verbal categories in general, the first semantic argument
(arg1) is linked with the first syntactic complement, the subject, figure 4.52.
This type is appropriate for intransitive verbs, where the subject NP, which is
the first syntactic complement, is linked with the first semantic argument. All its
subtypes inherit this information. However, the one-arg-raising-verb-linking
gendir
type does not follow this pattern,
since it defines that its argument is linked to
the second syntactic argument, which is the predicative complement, figure 4.53.
subjdir ndir2 vargdir
This is done using inequalities
which negate the inherited coindexation between
the subject and the first semantic argument. This type is appropriate for intrandetdir
ndir
sitive raising verbs, which do not assign a semantic role to the NP subject, their
first syntactic complement, but instead link their first semantic argument to the
second syntactic complement. An example is found in the sentence Bill seems to
run, where seems has only one semantic argument and it is linked to its verbal
intrans-sign
complement run.
The type two-arg-verb-linking inherits the linking constraint from the oneintrans-raising-sign
trans-sign oblique-intrans-sign
intrans-equi-sign
arg-verb-linking
type and adds
a further constraint that the second semantic
role, arg2, is linked to the second syntactic complement, figure 4.54. In the case
oblique-trans-sign
ditrans-sign
trans-raising-sign
trans-equi-sign
85










one-arg-verb-linking

CAT:ACTIVE : <! np-sign
SIGN:SEM:INDEX
SEM:RESTR : <! ARG1 : / 1 ! >




! > 


: / 1




Figure 4.52: One-arg-verb-linking Type












intrans-raising-linking

CAT:ACTIVE : <! np-sign
SIGN:SEM:INDEX


SEM:RESTR : <! ARG1 : 2 / 1 ! >
: / 1
 
, 
intrans-sign
SIGN:SEM:INDEX
2 6↔ 1
:




! > 


2






Figure 4.53: Intrans-raising-linking Type
of transitive verbs, the second syntactic complement corresponds to the direct
object and in the case of intransitive equi verbs to the predicative complement.
More linking constraints are introduced by the type three-arg-verb-linking,
which determines that the third semantic role (arg3) is linked to the third syntactic complement (figure 4.55). This is appropriate for both oblique transitive
verbs, where the third subcategorised element is an oblique object, and ditransitive verbs, where the third subcategorised element is the indirect object.
As in the case of the verbal semantic hierarchy, the use of a default inheritance hierarchy for encoding a linking theory resulted in generalisations being
concisely defined only once, in more general types and being propagated to more
specific types. Moreover, the use of default specifications provided a means of
implementing subregularities, such as the intrans-raising-linking type.
The Signs
The three different hierarchies defined for syntactic, semantic and linking information are combined together in the hierarchy of signs. Thus, an intransitive
verb of type intrans-sign is cross classified as:
• intrans, which is a type in the syntactic hierarchy that defines the need
for one subcategorised complement,







two-arg-verb-linking
CAT:ACTIVE : <! > , SIGN:SEM:INDEX
SEM:RESTR : <! ARG2 : / 2 ! >
: / 2
Figure 4.54: Two-arg-verb-linking Type
86



!>










three-arg-verb-linking
CAT:ACTIVE : <! > , > , SIGN:SEM:INDEX
SEM:RESTR : <! ARG3 : / 3 ! >
: / 3



!>



Figure 4.55: Three-arg-verb-linking Type
• one-arg-sem, which specifies the requirement for one semantic argument
in the semantic hierarchy, and
• one-arg-verb-linking type, which in the linking hierarchy maps the first
semantic role to the first subcategorised element.
The resulting intrans-sign type is shown in figure 4.56, with only the relevant
features being shown, and a fragment of the verbal sign hierarchy is shown in
figure 4.57.


























































intrans-sign
ORTH : orth
 intrans
CAT














: 
















SEM






: 






RESULT:SIGN:CAT

ACTIVE





: <!










: 





CAT-TYPE : s-cat

sent-m-feats  



M-FEATS :  VERB : true  
AUX
:
false



INV : false


np-sign


SIGN

CAT : np

SEM:INDEX : 1

DIRECTION :  subjdir
DIR-VALUE


: 

:
backward
one-arg-sem


MODE : prop


INDEX : index






 RELN : reln 



RESTR : <! SIT : index ! > 
ARG1 : 1






































! > 






























Figure 4.56: Intrans-sign Type Expanded and DefFill ed
Default specifications play a major role in the hierarchies, allowing subregularities and exceptions to be straightforwardly defined in a concise encoding.
As a consequence of using multiple inheritance hierarchies, these three different kinds of linguistic information are contained in three different hierarchies,
which interact with one another combining their information at the level of signs.
This modularity means that any subsequent change or addition to any of these
hierarchies will be localised, not affecting the others.
87
gendir
subjdir
ndir2 vargdir
detdir
ndir
intrans-sign
intrans-raising-sign trans-sign oblique-intrans-sign intrans-equi-sign
oblique-trans-sign
ditrans-sign
trans-raising-sign
trans-equi-sign
Figure 4.57: Fragment of the Verbal Sign Hierarchy
4.3
Rules
Rules are defined as typed feature structures that represent relationships between
two or more signs. There are three different types of rule implemented: morphological, lexical and grammatical. Morphological and lexical rules are unary rules
used for generating derived or inflected items from the lexical entries encoded in
the lexicon; they are discussed in section 4.3.1. Grammatical rules are used to
combine constituents together; they are described in section 4.3.2.
4.3.1
Morphological and Lexical Rules
Morphological and lexical rules are implemented using asymmetric unification,
following Briscoe and Copestake [1999]. Using this approach a lexical entry that
is successfully unified with the input description of a lexical rule, is then default
unified with the output of the rule, where the input is treated as defeasible and the
output as indefeasible. The resulting sign has all the information in the output
of the lexical rule, plus all the information in the input that is consistent with
the output. However, all the information in the input that is inconsistent with
the output is removed, as explained in section 3.5. Morphological and lexical
rules, being unary rules, are represented throughout the document with an input
TDFS, specified in the attribute ‘1:node’, an output TDFS, in the attribute
‘node’, and a function for spelling change in the attribute ‘function’ (figure
4.58), using a notation similar to that employed in [Pollard and Sag 1987]. The
use of asymmetric unification ensures that the input and output categories are
related, with just some modification that follows from unifying the defeasible
input with the indefeasible output, rather than just copying substructures from
the input to the output structures, which are not necessarily related.
Morphological rules are treated as a special case of lexical rules, potentially involving affixation and, consequently, being applied before parsing. Rules
of this kind that capture both nominal and verbal inflections are defined. One
such rule is the plural-noun-rule. Since noun lexical entries are defined as
having a third person singular agreement by default, the plural-noun-rule generates plural forms from these third person singular nouns, adding the appropriate
88





















plural-noun-rule

 ORTH : 1
NODE :  CAT :  noun
M-FEATS:AGR

:
FUNCTION
: f-pl-noun( 2 , 1 )

ORTH
: 2

1:NODE :  CAT :  noun
M-FEATS:AGR

























non-3sg
:
3sg
Figure 4.58: Plural Noun Morphological Rule























noun-sign
ORTH : <!dog! >
noun

CAT
SEM





: 





:
M-FEATS
noun-sem






: 




PRON : false 


LOC : false


WH : false

COUNT : true 
AGR : 3sg























Figure 4.59: dog Sign
suffixes and specifying the required agreement values (figure 4.58). In pluralnoun-rule the input is a noun with agreement defined as third person singular
(cat:m-feats:agr:3sg). When the defeasible input is unified with the indefeasible output specification, the input agreement information is incompatible with
non-3sg and consequently absent from the resulting TDFS, which contains the
indefeasibly defined non-3sg. However, all the remaining information from the
input is present in the result TDFS. For instance, when the lexical entry for dog
(figure 4.59), is given as input to this rule, the resulting output sign contains the
plural form dogs (figure 4.60).
Verbal lexical entries are defined by default as being in the base form and
several rules are defined for generating the other inflected forms. One such case
is the rule 3sg-v-rule that generates the third person singular inflection from the
base form, including affixation when appropriate (figure 4.61). Similarly the rule
non3sg-v-rule generates lexical entries that define the other person and number
agreement cases (figure 4.62). Both these rules specify the appropriate agreement
for the subcategorised NP subject. Other finite forms are also generated from
the base form. For example, past-prt-v-rule generates past participle forms
(figure 4.63), and past-v-rule generates past forms, with these rules including
appropriate affixation when necessary.
The resulting set of rules, defined with asymmetric unification, is more concise
and clear than a traditional equivalent, where much more information would need
to be defined in each of the rules. Moreover, with the use of default specifications
89
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












plural-noun-rule

 ORTH :





<!dogs! >



 

 
noun


 




 






 PRON : false



 




 

 LOC : false


 
NODE :  CAT :  M-FEATS :  WH : false
 

 



 




 
 COUNT : true  








 

 
AGR
:
non-3sg

 

 


SEM : noun-sem



FUNCTION
: f-pl-noun( 2 , 1 )





 ORTH : 2 <!dog! >





noun
















 PRON : false








: false

1:NODE :  CAT :  M-FEATS :  LOC

WH
:
false











 COUNT : true  











AGR
:
3sg





SEM : noun-sem
1
Figure 4.60: Plural Noun Morphological Rule Applied to dog
























3sg-v-rule





 ORTH : 1





: fin

NODE :  CAT :  RESULT:SIGN:CAT:M-FEATS:VFORM

 ACTIVE : <!


!
>

SIGN:CAT:M-FEATS:AGR : 3sg


FUNCTION
: f3rdsg-verb( 2 , 1 )

 verb-sign
1:NODE :  ORTH : 2

CAT : RESULT:SIGN:CAT:M-FEATS:VFORM

:
base

















Figure 4.61: Third Singular Verb Morphological Rule





















non3sg-v-rule

NODE



: 


CAT




: 









!>















RESULT:SIGN:CAT:M-FEATS:VFORM
: fin
ACTIVE : <! SIGN:CAT:M-FEATS:AGR : non3sg
FUNCTION
 :
verb-sign
1:NODE :  CAT : RESULT:SIGN:CAT:M-FEATS:VFORM
:
base
Figure 4.62: Non Third Singular Verb Morphological Rule
90



















prt-v-rule







NODE :  ORTH : 1


CAT:RESULT:SIGN:CAT:M-FEATS:VFORM : prt



FUNCTION
: fpast-prt-verb( 2 , 1 )




verb-sign




1:NODE :  ORTH : 2


CAT:RESULT:SIGN:CAT:M-FEATS:VFORM : base 
Figure 4.63: Past Participle Verb Morphological Rule





























inv-rule 
NODE


: 

CAT


: 

RESULT:SIGN:CAT:M-FEATS:INV
: true
ACTIVE : < DIRECTION:DIR-VALUE : forward
FUNCTION
:

verb-sign


1:NODE





: 





CAT




: 



RESULT:SIGN:CAT:M-FEATS
ACTIVE

: <

: 

AUX : true 
INV : false
SIGN: : np-sign
DIRECTION:DIR-VALUE
:





>
backward












>





























Figure 4.64: Inverted Modal Rule
in the basic lexical entries, fewer rules have to be defined. In this case, rules for
generating base form verbal signs and for generating third person singular forms
for nouns do not need to be defined, since these forms are defaults in the type
definitions, with verbs as vform:/base and nouns as cat:m-feats:agr:/3sg.
Lexical Rules are applied lexically, either before and/or after affixation or
during parsing, as appropriate. Among the rules defined, verbal lexical rules
create lexical entries from a basic canonical form. For instance, the inv-rule
generates the inverted form of a verb which is appropriate for capturing yes-no
questions, where the auxiliary verb is fronted preceding the subject: Will you buy
this car?, figure 4.64. The category of the auxiliary verb will is changed from
(S\NP)/(S\NP) to (S/NP)/(S\NP).
The imperative-rule generates the imperative form for verbal categories (figure 4.65), for capturing sentences like Put that down, where the subject is not
explicitly realised. This rule removes the subject category from the subcategorisation list and marks the agent role in the semantic specification of the sentence
as an imperative one (imp-index). Because this rule is implemented with asymmetric unification, inequalities need to be used to negate the existing default
coindexations between the corresponding elements in the subcategorisation list
in the input and output descriptions.
Following Briscoe and Copestake [1999], lexical rules are also defined for generating the dative alternation (figure 4.66). The dative-rule generates the dative
construction from the oblique frame of a verb. The result of applying this rule
91

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
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
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
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



imperative-rule


NODE





: 





CAT
SEM

: 


: 

ACTIVE
: <!
0 6↔ 1
SIGN
MODE : imp
RESTR : <! ARG1
0 / 1
:
:
!>

imp-index






!>











FUNCTION
:

verb-sign




RESULT:SIGN:CAT:VFORM : base


1:NODE :  CAT :  ACTIVE : <!

SIGN : np-sign/ 1 , SIGN


SEM:MODE : prop

:







!>

0


































Figure 4.65: Imperative Rule















dative-rule

dative-sign
NODE :  CAT:ACTIVE
1:NODE


: 

: <!
>
,
>
,
SIGN
:
oblique-trans-sign
CAT:ACTIVE : <! > , > , SIGN
np-sign
:


!>
pp-sign





!>














Figure 4.66: Dative Rule
to an oblique verb (((S\NP)/NP)/PP) is that the oblique PP object is replaced
by an NP object in the dative type (((S\NP)/NP)/NP).
Two rules are defined to account for the case of passivisation. The first one,
the passive-rule, takes verbs (transitives or verbs with higher transitivity) and
generates the passive equivalent with the oblique argument (The vase was broken
by him), figure 4.67. The second rule, passive-no-by, generates the passive form
without the oblique argument which corresponds to the subject of the active form
(The vase was broken), figure 4.68. It also marks arg1 as having a null-index,
since the agent role is not realised syntactically. These rules also require the
use of inequalities to negate the default coindexation that exists between the NP
subjects in the input and output subcategorisation lists, since they do not have
conflicting values.
These are some of the morphological and lexical rules defined and a fragment
of the set of rules is included in Appendix B.
4.3.2
Grammatical Rules
In CG some of the categories can be viewed as arguments and some as functions,
and the set of rules is responsible for combining functions with arguments or with
other functions. In this work five rules are defined: forward application, backward application, forward composition, backward composition and generalised
92
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


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
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

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



























































passive-rule

NODE
















: 
















CAT

: 







6
3
 1 ↔
6
2 ↔
4
SEM:RESTR
FUNCTION

1:NODE
 RESULT:SIGN:CAT:M-FEATS:VFORM





 np-sign
 ACTIVE : <!
SIGN
:


SEM:INDEX : 1











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

: 












pass

:

CAT








: 












SIGN
RELN
ARG1
ARG2
:



:

: <!
:


 2 6↔ 3
1 6↔ 4
: 
pp-sign
SEM:INDEX
:
2
:


,



!>
reln 

2



! >



1
trans
RESULT:SIGN:CAT:M-FEATS:VFORM


ACTIVE : <! SIGN :  np-sign
SEM:INDEX : 3

SEM:RESTR



: <!



SIGN
RELN
ARG1
ARG2

: 
np-sign
SEM:INDEX
:
4

reln 
:
:
3
:
4









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

























prp  
:


,


! >













! >































































































Figure 4.67: Passive Rule





















































passive-no-by-rule



 RESULT:SIGN:CAT:M-FEATS:VFORM







np-sign
 CAT : 
 ACTIVE : <!
SIGN
: 




SEM:INDEX : 1



NODE : 






1 6↔ 0
SEM:RESTR

: <!
ARG1
ARG2
:
:
pass
:


! >

null-index ! >
1

















FUNCTION
:


 trans-sign






RES:SIGN:CAT:M-FEATS:VFORM
: prp


 












np-sign





 ACTIVE : <! SIGN : 
,  




0
SEM:INDEX
:

 CAT : 








1:NODE : 






np-sign



 ! > 


SIGN
:





SEM:INDEX
: 1









SEM:RESTR

: <!
ARG1
ARG2
:
:

0 
!>
1
Figure 4.68: Passive without Oblique Argument Rule
93








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





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
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
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




weak permutation. These rules are defined as types in the grammar, in terms of
TDFSs. The binary rules of application and composition have two input TDFSs
defined, respectively, in ‘1:node’ and ‘2:node’, according to the linear order of
the constituents to be combined. The output TDFS, which is the result of the
combination of the input TDFSs, is defined in ‘node’. The unary rule of GWP
has one input TDFS defined in the attribute ‘1:node’, and an output TDFS defined in ‘node’. Moreover, in these rules ‘...’ represents one or more arguments
in the subcategorisation list.
In the complex categories defined, the subcategorised arguments are ordered
in the active list, with the first element in the list being the one considered for
combination with adjacent categories.
The Functional Application rule simply combines a function with its argument, as explained in section 4.1:
• Forward Application: X/Y Y → X is encoded as shown in figure 4.69,
where the category X/Y, to the left, is represented in the attribute 1:node;
the category Y, to the right, is represented in 2:node; and the resulting
category X is represented in node.
• Backward Application rule: Y X\ Y → X is encoded as in figure 4.70.










































forward-application

ORTH :

<! 0 , 1 ! >








RESULT:SIGN:CAT : 2 cat
ACTIVE : <![...] 3 ! >
SEM:RESTR : <! 4 , 5 ! >

ORTH : <! 0 , 6 ! >



: 2
 RESULT:SIGN:CAT






SIGN:CAT
: 7
1:NODE:SIGN :  CAT :  ACTIVE : <!
DIRECTION:DIR-VALUE


NODE:SIGN



: 



CAT




2:NODE:SIGN
:



: 

SEM:RESTR : <! 4
ORTH
: <! 6 , 1 ! >


 CAT : 7 cat

SEM:RESTR : <! 8
[...]
3
!>
, 8 !>


, 5 !>

:
forward




 



, 











Figure 4.69: Forward Application
Functional application captures a wide range of constructions, being used to
combine, for example, verbs with their complements, determiners with nouns,
and adjective with nouns, among others.
The rule of Functional Composition allows a functor category missing an
argument to compose with an adjacent function that outputs that argument as
its result:
94
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











backward-application

ORTH :

<! 0 , 1 ! >








RESULT:SIGN:CAT : 2 cat
ACTIVE : <![...] 3 ! >
SEM:RESTR
: <! 4 , 5 ! >



 ORTH : <! 0 , 6 ! >


1:NODE:SIGN :  CAT : 7 cat


SEM:RESTR : <! 8 , 5 ! >

ORTH : <! 6 , 1 ! >



: 2

 RESULT:SIGN:CAT






 ACTIVE : <! SIGN:CAT : 7
2:NODE:SIGN :  CAT : 
DIRECTION:DIR-VALUE


NODE:SIGN



: 



CAT







: 

SEM:RESTR
[...]
3

:
backward
!>
: <! 4 , 8 ! >




 



,  







Figure 4.70: Backward Application
• Forward Composition: X/Y Y/Z → X/Z (figure 4.71).
• Backward Composition: Y\Z X\Y → X\Z.













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
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









forward-composition

ORTH :

<! 0 , 1 ! >








RESULT:SIGN:CAT : 2 cat
ACTIVE : <![...] 3 , [...] 4 ! >
SEM:RESTR : <! 5 , 6 ! >

ORTH : <! 0 , 7 ! >



: 2

 RESULT:SIGN:CAT





SIGN:CAT
: 8
1:NODE:SIGN :  CAT :  ACTIVE : <!
DIRECTION:DIR-VALUE


NODE:SIGN



: 



CAT




2:NODE:SIGN

: 

[...]
3
!>
SEM:RESTR : <! 5 , 9 ! >
ORTH
: <! 7 , 1 ! >





 RESULT:SIGN:CAT
 CAT : 

ACTIVE : <![...] 4 ! >


SEM:RESTR : <! 9 , 6 ! >

:


:


:
forward




 



, 









8 





Figure 4.71: Forward Composition
Functional composition is used mainly to capture unbounded dependencies
and coordinations, since it allows non-conventional constituency.
The unary rule of Generalized Weak Permutation allows a complex category to combine with its arguments in any order, as is discussed in section 4.4.
GWP rotates the arguments of a complex category, with the number of possible
permutation operations being finite and bounded by the number of arguments
95
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

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
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
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
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










the category has. While rotating the arguments, this rule maintains the original
direction associated with each of them.
• Generalised Weak Permutation (P): ((X|Y1 ) . . . |Yn ) → (((X|Yn )|Y1 ) . . .),
shown in figure 4.72

























generalised-weak-permutation





ORTH : <! 0 , 1 ! >









cat
RESULT
:
2


NODE:SIGN :  CAT : 





ACTIVE
: <! 4 , 3 , [...]! >





SEM:RESTR : <! 5 , 6 ! >





ORTH
: <! 0 , 1 ! >









1:NODE:SIGN :  CAT :  RESULT : 2 cat



ACTIVE
: <! 3 , [...], 4 ! >



SEM:RESTR : <! 5 , 6 ! >

Figure 4.72: Generalised Weak Permutation
The arguments in the subcategorisation list are ordered and the first argument is the one considered for combination with adjacent categories. Thus, if
the order of elements in the subcategorisation list does not allow a category to
be combined, the subcategorised arguments are rotated until the argument required for combination is in the first position. For instance, for verbal categories,
the subject is always the first element in the subcategorisation list (followed by
the direct object, indirect object and so on, as required for a particular verbal
category). This is defined in the intransitive type (intrans) and inherited by
all verbal types in the syntactic hierarchy. In this initial ordering, the subject is
always the first to be combined in any verbal category. In an atomic representation of the categories, for instance, a transitive verb following this ordering is
represented as S/NPO \NPS . 5 For some sentences, this initial ordering is not
appropriate and does not produce a derivation. In these cases, the GWP rule is
necessary to rotate the elements in the subcategorisation list until an appropriate
ordering is achieved. One example is the case of the coordination in the sentence
He bought fish and cooked dinner, whose derivation is shown in figure 4.73. Both
verbs have category S/NPO \NPS and need to be combined with their direct objects first. This is achieved by rotating the arguments so that the object (NP O )
is the first in the subcategorisation list: S\NPS /NPO .
This rule allows the grammar to capture more flexible word orders, without
the need for defining extra categories. As a result the grammar can capture, for
example, verb-particle constructions where the particle can be either before or
after the object, using the same category. For instance, the verb back, which
has category ((S/PRT)/NP)\NP and takes the particle up, not only accepts a
5
In the remainder of this document this ordering is adopted.
96
"!
#$%
&
( )*"%
-
% $)$)+
&
-
,
'
'
Figure 4.73: Derivation of Sentence He bought fish and cooked dinner
sentence such as Bob backed the team up (figure 4.74) which follows the initial
word order specified, but also accepts Bob backed up the team, when its subcategorised arguments are rotated (figure 4.75). On the other hand, by accepting
freer word orders this rule can also overgenerate. This is the case, for example, of
verb-particle constructions that have a fixed order and only accept the particle
in a certain position in relation to the verb. This rule overgenerates, accepting
both the grammatical and the ungrammatical orderings, such as in She came up
with the idea and *She came with the idea up, respectively.6 Moreover, for categories which subcategorise for similar categories with the same directions, this
rule allows derivations where the categories are interchanged. This is the case
of ditransitive verbs, for example, with category ((S/NPO2 )/NPO1 )\NPS , where
the two NP objects are to the right: NPO1 corresponds to the direct object and
NPO2 to the indirect object. GWP also allows NPO1 to be linked with the indirect
object and NPO2 to the direct object. Thus, a sentence such as He gave Cathy a
flower has two different logical forms generated. The first one is where Cathy is
the indirect object being linked with the recipient role, and a flower is the direct
object being linked with the patient role, where a flower is given to Cathy. In
the other, a flower is the indirect object being linked with the recipient role and
Cathy is the direct object linked with the patient role, where Cathy is given to a
flower. In spite of this overgeneration caused by the GWP rule, the benefits that
it brings in terms of the coverage obtained without the need for extra categories,
greatly outweighs that. Furthermore, there are possible ways of constraining the
application of this rule to control overgeneration. For instance, one way of doing
this while at the same time ensuring termination is to store, for each category,
the number of arguments it has, and maintain a count of the number of times the
arguments are rotated against the maximum number of possible operations for
the category, which is obtained by subtracting one from the number of arguments.
In this way, the application of GWP is bound by the number of arguments of
a category, and for a category such as ((S/NPO2 )/NPO1 )\NPS , for ditransitive
verbs, containing 3 arguments, only 2 applications of GWP are allowed, generat6
Ungrammatical sentences are marked with *.
97
ing the following categories besides the original one:
((S\NPS )/NPO2 )/NPO1
((S/NPO1 )\NPS )/NPO2
## $
% "!
"
)
&
'
(
(
(
Figure 4.74: Derivation of Sentence Bob backed the team up
*+,
89
,-./01
243
5$60
:#:;<9=>?<$8'9? @ 89
9=>
8'9"<$8
:#;<9=>?C<89
D
;<89
8
89
B
:#;<89?<$9=>
5#0-"7
A
A
;
A
Figure 4.75: Derivation of Sentence Bob backed up the team
These grammatical rules are used to combine or allow the combination of
constituents and the result of a derivation using the backward application rule is
shown in figure 4.76, for the sentence Bill runs. In this figure, both the orthography (orth) and the semantics (sem:restr) of the resulting sign contain the
conjunction of the orthographic and semantic specification of the signs that were
combined. This conjunction is obtained through the use of difference lists, which
append the signs being combined according to the rule definition: node:orth:<
! 0 , 1 ! > = 1:node:orth:<! 0 , 6 ! > + 2:node:orth:<! 6 , 1 ! >.7
4.4
Coverage
The implemented UB-GCG has 89 lexical categories defined, covering several
linguistic constructions. For instance, it can handle several verbal constructions,
it captures declarative, imperative and interrogative sentences, and successfully
treats constructions such as unbounded dependencies (wh-questions and relative
7
Throughout this document, for reasons of clarity, the atomic formulation of the rules will
be used, unless otherwise required.
98






















NODE
:


sign



 ORTH : <!bill, runs! >





 CAT : s








MODE
:
prop











 INDEX : 1  index



 






 SEM : 


RELN
:
run
SIT
:
3
index













 RESTR : <!


! > 
,  NAME : bill
SIT : 1






 





ARG : 2 index
NAMED : 2


Figure 4.76: Sentence Bill runs
clauses) and coordinations. The lexical categories encode the relevant linguistic
information and they are defined in terms of five basic categories (S, NP, N,
PRT and PP) and three operators (forward and backward slashes and product
operator). In this section, the treatment given in the implemented UB-GCG to
some of these constructions is discussed.
4.4.1
Verbal Constructions
Most verbal constructions are implemented in the grammar directly as lexical
category types and assigned to the appropriate lexical entry for a verb. Thus the
verb loves in the sentence John loves Mary is a transitive verb, with category
S/NP\NP, and one derivation for this sentence is shown in figure 4.77.
!
"
Figure 4.77: Derivation for a Transitive Construction
Similarly oblique transfer verbs and dative verbs are defined as types in the
verbal hierarchy. However, following Briscoe and Copestake [1999] these verbs
are treated as part of a family of dative constructions, which have the same
syntactic and related semantic properties [Goldberg 1995]. Most lexical entries
will be of type oblique-trans-sign, for oblique transitive verbs with category
((S/PP)/NP)\NP. For example, the verb give, which occurs in oblique transitive
constructions, such as the sentence Bill gave the dog to Mary. The dative alternation is captured by the dative lexical rule, which maps an oblique-trans-sign
into a dative-sign with category ((S/NP)/NP)\NP. Then one possible derivation for the sentence Bill gave Mary the dog is shown in figure 4.78, where the
dative lexical rule is represented in the derivation as Dat Rule. The thematic
roles are correctly linked to the syntactic arguments, with Bill being linked to the
99
!
"$# %&%&')(*##+,( "$#+ - " # "/# "$#.(" "
0
"$#
%&%&')(*"$#+,("$#+ - "$#
1
%&')("$#+,("$#
0
' ( "$#
0
'
Figure 4.78: Derivation of Sentence Bill gave Mary the dog
:; < <
=*>&; [email protected]
C= B
7$8 F5 2G4&5&2 6 7$89&9 6 7$8 5&2 6 7$
8 9,4C5F2 6 $
7 89
2)4C5&2 6 7/89
I
H
2)4&5&2 6 7$89
3
2
>&DE
2 6 7$8
3
Figure 4.79: Derivation of Sentence Bill tries to run
agent role (arg1), the dog to the patient (arg2) role, and Mary to the oblique
role (arg3).
Raising and equi constructions are represented by appropriate types defined in
the verbal hierarchies. In the case of intransitive (or subject) equi verbs, such as
try, with category (S/(S\NP))\NP, its subject is also the subject of the embedded
verb. One possible derivation for the sentence Bill tries to run is shown in figure
4.79. As can be seen in the logical form for this sentence (figure 4.80), both the
control and the embedded verb assign a semantic role to the shared subject.
Intransitive raising verbs are similar to equi verbs, also with category
(S/(S\NP))\NP, except that the subject of the embedded verb is not assigned a
semantic role. This can be seen in one derivation for the sentence Bill tends to
run, shown in figure 4.81, and in the corresponding logical form, in figure 4.82.
The infinitival to is also treated as a raising verb with category (S/(S\NP))\NP.
The same patterns are observed with transitive (or object) control verbs,


























sem


MODE : prop


INDEX : 0  index




 

RELN
: try



RELN
:
to

 
 
 
 
RESTR : <! SIT : 0
,  SIT : 2
, 




 ARG1 : 1 index 
ARG1 : 3 index 
ARG2
: 2 index

 





 RELN : run   SIT : 4 index 

 



,  NAME : Bill
! >
 SIT : 3

 



ARG1 : 1
NAMED : 1
Figure 4.80: Logical Form of Sentence Bill tries to run
100
Figure 4.81: Derivation of Sentence Bill tends to run























sem


MODE : prop



INDEX : 0  index
 
 


 RELN : tend
 
  RELN : to

 
 
RESTR : <! SIT : 0
, 
,  SIT : 1
 
 


ARG1 : 1 index  ARG1 : 2 index





RELN
:
run
SIT
:
4
index



 


 


 SIT : 2
! >
,  NAME : Bill



 

ARG1 : 3 index
NAMED : 3

Figure 4.82: Logical Form of Sentence Bill tends to run
except that it is the object of a transitive control verb that controls the subject
of the embedded verb.
Verbs that expect a particle have an extra argument, with category PRT, in
the subcategorisation list. For instance, the transitive particle taking verb warm
has category ((S/PRT)/NP)\NP. When combined with the particle up, the verb
can be either immediately followed by the particle, as in warm up the milk, or be
followed by the direct object and then by the particle, as in warm the milk up.
These two cases are captured using the same category, but in the first case using
the permutation rule, as shown in figures 4.83 and 4.84. Figure 4.85 shows the
specification of the verb warm with the particle up. These cases differ from those
where verbs take a complete PP as complement. For example, the verb put has
category ((S/PP)/NP)\NP and a derivation for the sentence He put the book on
the shelf can be seen in figure 4.86. In this case, the preposition, with category
PP/NP, needs to be combined first with its NP complement to be then combined
with the verb.
"!$# %$& '
(")+*,./ 0
132' 4
, &#5
6
7 889:37;=<?>:@67> A 67 7
; < 67$:@6
6
E
B
6
7
89:37;=<?>:@67
C
89:36
7>D:@7;<
9:@67
B
9
B
Figure 4.83: Derivation of Sentence Goldie warms up the milk
101
'
'
( +
"#$
% &
!
'
'
)
*
)
)
Figure 4.84: Derivation of Sentence Goldie warms the milk up

















trans-prt-sign

CAT






: 





RESULT:SIGN:CAT:M-FEATS
ACTIVE
: <!
>
,
>

SIGN

,
:


sent-m-feats

TAKE-PARTICLE : true 
PARTICLE : 1 up

 particle-sign
CAT:M-FEATS:P-FORM : 1


: 

Figure 4.85: Abbreviated Lexical Entry for warm, with pform:up
897
3'0
:<; 5
56$7
3'0/3
--./00*12/3'01 4 3'0
-./0012/3'0
E
30
./00
=?>!>@
>A
3
00/3'0
56$7
3'0/3
,
,
3'0
00
B 6?7<C D
3
,
,
,
.
Figure 4.86: Derivation of Sentence He put the book on the shelf
102
















 ! >  


!/ 0213(+*-,. " $
4 $
#
$
%
&
)
'
+
(
*
,.
Figure 4.87: Derivation of Sentence Give me that pillow
56+7 8 9;:<>=6
9;:8
?CB"DE"6F< [email protected] HG :[email protected]
QR"N
Q Q T L MN>LOM P QRSS P QV R LMNQ#RS P QR V RR"N
QR Q R T
QR
L M P Q#RSbN>LM P Q#RS LOM P QRSN
QR T
RR
LM P QRSNQR
a
VWYX X[Z]\^Y_`
LOM P QRSN
RR
T
M P QR
U
M
Figure 4.88: Derivation of Sentence This watch was bought by Mary
Imperative sentences are captured by having a lexical rule that applies to
the main verb, removing the subject NP from the list of subcategorised elements and marking the agent role as implicit. Figure 4.87 shows one derivation for the sentence Give me that pillow, where the initial category for give is
((S/NPO2 )/NPO1 )\NPS and where NPS is removed after the application of the
imperative lexical rule (Imp Rule in the derivation).
Passive sentences are also captured by means of lexical rules that relate them
to their active counterparts, so that the semantic roles of the arguments of the
active and passive pairs are the same. However, the syntactic realisation of these
roles is different, with the subject of the passive corresponding to the object of the
active and the subject of the active, if present at all in the passive, corresponding
to the argument of the prepositional phrase containing the preposition by. For
instance, in the sentences This watch was bought by Mary (passive) and Mary
bought this watch (active), the subject of the first sentence is this watch, while in
the second it is Mary. However, in both cases the agent role of bought (arg1)
should be linked to the predicate associated with Mary. Figures 4.88 and 4.89
show derivations for the first and second sentences, respectively, where Pass
Rule represents the passive lexical rule.
Auxiliary verbs are encoded as types in the verbal hierarchies which capture
the generalisation that auxiliaries take verbal complements. Moreover, different
auxiliaries require different forms of verbal complements. For instance, have requires a past participle verbal complement (Jane has studied English literature),
while be requires a progressive form (Jane is studying English literature). This
103
!"#%$ & #
'
!"#
#
(
(
Figure 4.89: Derivation of Sentence Mary bought this watch







aux-prp-sign
CAT:ACTIVE : <! > ,
SIGN:CAT:RESULT:SIGN:CAT:M-FEATS:VFORM

:
prp
!>






Figure 4.90: Sign for the Auxiliary have
constraint is encoded in the vform attribute of the subcategorised verbal complement, as shown in figure 4.90 for have. In terms of semantics, auxiliaries are
treated as raising verbs, not assigning a semantic role to their subjects.
Interrogative sentences are handled by means of lexical rules. In this kind of
sentence, a finite auxiliary verb precedes the subject (Will Mary buy the car? ).
This constraint can be easily and straightforwardly achieved by changing the direction of the subject NP from ‘backward to ‘forward. This is done by a lexical
rule (Inv Rule) that has as input an auxiliary with category (S/(S\NP))\NP
and generates as output the category (S/(S\NP))/NP. One derivation for the
sentence Will Mary buy the car? is shown in figure 4.91.
4.4.2
Unbounded Dependencies
The term Unbounded Dependencies refers to the several families of natural
language constructions where there is a relationship among distant subexpressions
within an expression. In these constructions a fronted constituent can “belong
to” another constituent embedded arbitrarily deep. For instance, in the sentences
Who do you like?, Who do you think you like?, Who does Jane believe you like?
and Who does Kate say Jane believes you like? the distance between who and
the position it binds, as the object of like, is embedded deeper and deeper in each
>@? A A
) *!+),* - .#/%0 0 - .#/
*!+) * - .#/%0L+.#/
1234
5674
8"9:
. /
) * - ./%0<+".#/
B CDFEHGIFJ K
=
*!+) * - .#/%0
;723
.#/+".
.
.#/
=
* - .#/
=
=
*
Figure 4.91: Derivation of Sentence Will Mary buy the car?
104
>
>
S\NP
S
Who
does
Jane
hate
S/(S/NP) (S/(S\NP))\NP NP (S/NP)\NP
Inv Rule
P
(S/(S\NP))/NP
(S\NP)/NP
>
Who S/(S\NP)
does
love
Bill
B>
S/(S\NP) (S/(S\NP))\NP
(S/NP)\NP
S/NP
>P NP
P
S
(S\NP)/(S\NP)
(S\NP)/NP
>
S\NP
>
S\NP
>
S
Figure 4.92: Derivation of Sentence Who does love Bill?
does
Jane
hate
Where Who did
John
put
the keys
S/(S/NP)
(S/(S\NP))\NP
NP (S/NP)\NP
S/(S/PP)
(S/(S\NP))\NP
NP (S/PP)/NP\NP
NP/N
N>
P
P
Inv. Rule Inv Rule
(S/(S\NP))/NP
(S\NP)/NP
(S/(S\NP))/NP
(S\NP)/PP/NP
NP
>
>
>
S/(S\NP) (S\NP)/PP
S/(S\NP)
B>
B>
S/PP S/NP
>
>
S
S
Figure 4.93: Derivation of Sentence Where did John put the keys
of them. CGs are well known for providing a simple and elegant way of capturing
8
unbounded dependenciesWhere
. In this section,
the treatment
given
did
John
put
the for
keyswh-questions
and relative clauses isHow
discussed.
S/(S/PP) (S/(S\NP))\NP
NP (S/PP)/NP\NP
does
Helen
look P NP/N N >
Inv.
Rule
In wh-questions,
wh-words
have
complex
categories
take >as argument
(S/(S\NP))/NP
(S\NP)/PP/NPthatNP
S/(S/(NP\NP)) (S\NP)/(S\NP)
NP
(S\NP)/(NP\NP)
>
S/(S\NP)
(S\NP)/PP
a sentence missing a constituent and whose
result is an S category.
There are
Inv. Rule
B>
S/PP
several different constructions,(S/NP)/(S/NP)
corresponding
to
different
extraction
patterns
for
P
>
S/(S\NP)/NP
S
the fronted object. For each of these constructions,
an appropriate category is
>
S/(S\NP)
defined. Thus for Subject Extraction, exemplified in sentence
4.8, the fronted
B>
S/(NP\NP)
wh-pronoun (who) corresponds to the subject of the verb (love),
and the pronoun
>
S
is assigned category S/(S\NP), as shown in figure 4.92.
• (4.8) Who does love Bill?
Another case of verbal argument
extraction
is Helen
that of PP
How
does
lookExtraction, where
the fronted wh-pronoun S/(S/(NP\NP))
corresponds (S\NP)/(S\NP)
to a PP argument
of the verb. The pronoun
NP (S\NP)/(NP\NP)
is assigned category S/(S/PP). One derivationInv.ofRule
the sentence 4.9 is shown in
(S/NP)/(S/NP)
figure 4.93.
P
S/(S\NP)/NP
S/(S\NP)
• (4.9) Where did John put the keys?
>
S/(NP\NP)
S
B>
>
There is also the case of Adjunct Extraction, where the fronted wh-word
corresponds to an adjunct and is assigned category S/S. An example of this kind
8
For an extensive discussion of unbounded dependencies and other phenomena in CGs, see
Steedman [1985 to 2000].
105
of extraction can be seen in sentence 4.10 whose derivation is shown in figure 4.94.
• (4.10) Where does John live?
# $&%('&) *(+ , !"
- Figure 4.94: Derivation of Sentence Where does John live?
Relative clauses are noun modifiers, usually involving a relative pronoun
such as who, which or that. The different kinds of relative clauses are modelled
by different lexical category types. One case of relative clauses contains Subject Extraction, where the relative pronoun, with category (N/(S\NP))\N,
corresponds to the subject of the embedded verb. This is exemplified in sentence
4.11, whose derivation is shown in figure 4.95, where the relative clause who
loves Bill modifies the noun person.
• (4.11) The person who loves Bill hates Bob
Another case is that of Adjunct Extraction, exemplified in sentence 4.12
whose derivation is shown in figure 4.96. In this case the relative pronoun corresponds to an adjunct with category (N/(S/PP))\N.
• (4.12) The house where John lives has a garden
These are some of the unbounded dependencies captured in the grammar and
./10 12 03547698 :;/16
< 6>=04 ? @ < < 1/ A>B04 C? 6D
FLH"F F EGFIHEJ K FLM M K FN E JH"FLM K FL N F L EJ"H FLM K FL N F L
EGF K FMQHEJ K FLM E J K FLM!HGFL O E J K FLM!H"FL O
J K FL
J K FL
O
F KF
P
F
O
FL
P
J
Figure 4.95: Derivation of Sentence The person who loves Bill hates Bob
106
, -
%! !"#" $ &
! " $ % # !%" $ % %!
)
)
+
*
$ %"'.("
( $ %"'(&
&
*
*
$ %
$
+
*
%
+
Figure 4.96: Derivation of Sentence The house where John lives has a garden
each of these cases is encoded in an appropriate lexical category type. These
types are organised in a hierarchy according to their valence and to the type of
the subcategorised elements. In the lexicon, these pronouns are assigned as many
categories as necessary to describe each of the different constructions in which
they take part.
All these cases of unbounded dependencies are captured with the definition of
appropriate lexical category types, based on the treatment proposed by Steedman
[1985 to 2000], which is implemented in the wide-coverage grammars developed
by Doran and Srinivas [in press] and Hockenmaier et al. [2000]. The treatment
adopted in this work, however, differs from that proposed by Steedman because
he uses the type raising rule for capturing cases of unbounded dependencies. This
rule allows, for instance, the verbal category to be combined first with the NP subject, by type raising the NP, and then with the other subcategorised categories.
However, since we use the permutation rule that allows the verb to combine with
any of its arguments in any order, the effect required for such combination is
already obtained. By using GWP we avoid the problem with raising rules which
are recursive and, as a consequence, categories can be raised ad infinitum unless
these rules are constrained. The GWP rule, on the other hand, in spite of being
recursive, is bounded by the maximum number of arguments of a given complex
category and, consequently, will only be performed a certain number of times.
Moreover, the flexibility provided by the use of type raising can allow many unwanted derivations, as found by Murgatroyd [2000], who investigated the use of
prosodic phrasing to help resolve parsing ambiguity.
4.4.3
Coordination
Coordination is one of the best known linguistic applications of CGs. In this
section the treatment of coordination adopted is discussed, focusing on the socalled coordination of ‘like categories’, where the conjuncts being coordinated are
of the same category.
Coordination involves the combination of constituents using conjunctions like
and and or. The coordination of like categories is implemented using an approach
107
equivalent to that used in [Gazdar 1981], which regards a coordinate structure
as a string of any syntactic category composed of two or more substrings of that
category linked by a conjunction. To encode this generalisation, the polymorphic
functor category (X\X)/X is used, where X stands for any category. In the grammar different types are used to capture different instantiations of this category,
such as NP\NP/NP, ((S\NP)\(S\NP))/(S\NP) and S\S/S, among others. 9 A
derivation for the sentence My brother and sister gave me a book, that contains
a coordination, is shown in figure 4.97. This approach is similar to the ones
employed in [Carpenter 1998] and [Doran and Srinivas in press].
/10
$&23%546&2
+,
8 4 &2
7 7 .
9
)
-
"#
()*
( :
.
!
$%&%'
.
)
.
.
-
Figure 4.97: Derivation of Sentence My brother and sister gave me a book
Due to the weaker notion of constituency in CGs, this approach accounts not
only for the cases of constituent coordination, but also for those of non-constituent
coordination, which refers to the cases where the conjuncts do not correspond to
constituents in the more traditional sense. For instance, in the sentence Bill likes
and Jane hates popcorn, the conjuncts are composed of subjects and verbs in
Bill likes and Mary hates. Although they are considered valid constituents in
CGs, this is not the case for other formalisms that employ a more traditional
notion of constituency. In what follows, cases of constituent and non-constituent
coordination are discussed.
In the coordination of NPs, the conjunction is assigned category NP\NP/NP,
as shown in figure 4.98 containing a derivation of the sentence 4.13.
• (4.13) I like John and Mary.
For coordinating Ns, the category required for the conjunction is N\N/N,
as can be seen in figure 4.97 with a derivation of sentence 4.14.
• (4.14) My brother and sister gave me a book.
9
The use of the category (X\X)/X to treat coordinations causes overgeneration, as in the
case of the sentence *A man who walks and he talks which would be incorrectly treated as
a case of coordination of NPs.
108
I
NP
like
John
and
Mary
(S/NP)\NP
NP (NP\NP)/NP NP
<
>
S/NP
NP\NP
<
NP
>
S
I
NP
like
John
and
Mary
Figure 4.98:NP
Derivation
of Sentence
(S/NP)\NP
(NP\NP)/NP
NP
<
>
S/NP
NP\NP
<
NP
I like John and Mary
>
S
When coordinating Ss (sentence 4.15), the conjunction has category S\S/S
(figure 4.99).
John
ate
Kim
brought
a
pizza
and
NP
(S/NP)\NP NP/N
<
N
>
NP
(S\S)/S
• (4.15) Kim brought a pizzaS/NP
and JohnNPate a slice.
S/NP
>
S
a
NP/N
(S/NP)\NP
<
S
S\S
Kim
NP
brought
a
(S/NP)\NP NP/N
S/NP
S
<
pizza
N
NP
>
and
(S\S)/S
JohnS
ate
NP (S/NP)\NP
S/NP
>
a
NP/N
<
slice
N
NP
S
S\S
S
>
>
>
<
Figure 4.99: Derivation of Sentence Kim brought a pizza and John ate a slice
One case of verbal coordination is that of Right Node Raising (RNR) (sentence 4.16), where the conjunction has category ((S/NP)\(S/NP))/(S/NP), and
the conjuncts are of category S/NP (You read and I taped ) (figure 4.100).
• (4.16) You read and I taped the story.
'" $#&%!(""$#&%"$##&") $# " $#&%! ! ,
, *
!
*
"$#&%+" $#
,
!
*
Figure 4.100: Derivation of Sentence You read and I taped the story
RNR is another point where the approach to treat coordination we adopted
differs considerably from the one used in [Doran and Srinivas in press] and
[Steedman 2000]. These works use subject type raising in order to enable the
109
NP
slice
N
>
>
>
<
subject to be combined with the verb, forming a subject-verb conjunct, which
is then able to be coordinated. However, as the permutation rule allows the
arguments of a given complex category to be combined in any order, the effect
obtained is the same: the subject can be combined with the verb, resulting in
the subject-verb conjunct that is needed.
Another case of verbal coordination is shown in sentence 4.17, with
coordination of verbal conjuncts, where both conjuncts are composed
of transitive verbs (cooked and ate), and the conjunction has category
(((S\NP)/NP)\((S\NP)/NP))/((S\NP)/NP) (figure 4.101).
• (4.17) The man cooked and ate potatoes.
!#"
$#%&
'
(
"
'
*
)
(
(
)
Figure 4.101: Derivation of Sentence The man cooked and ate potatoes
A case where the verbal conjuncts have different subcategorisation requirements, is shown in sentence 4.18. The first conjunct is composed of an intransitive
verb and the second is composed of a transitive verb and its object. In this case,
the object is not shared between the conjuncts; it is actually part of the second
conjunct, since only the transitive verb requires a direct object (figure 4.102).
• (4.18) She smiled and gave him a gift.
.54687:9<; = 6
>
[email protected]
>
4 ;9
A
B ?C6
01F./01G--./012/-./01223-./012 --.31123012/01
01
H
IKJMLNPO Q
--.30123012/01
R
--./0123012301
-./012301
./01
-./012/*-./012
./01
.
?
B ; DE
0130
0
,
01
,
,
,
+
+
Figure 4.102: Derivation of Sentence She smiled and gave him a gift
110
To capture the case of a ditransitive verb with conjoined pairs of objects, the
approach proposed by Wood [1989] is adopted. In this approach the product
operator, ∗, is used to form a product from a pair of objects. The products resulting from each pair of objects are coordinated and can serve as argument to a
verb looking for a product. Thus, in the lexicon, ditransitive verbs also have the
category (S/NP*NP)\NP. This is the case of sentence 4.19, whose derivation is
shown in figure 4.103.
• (4.19) Jane gave Bob a dog and Sue a cat.
/ "#
*+
,
+
.
-,
!
"#!
%$ 0
,
&')(
0
.
Figure 4.103: Derivation of Sentence Jane gave Bob a dog and Sue a cat
These are only some of the constructions that are captured in the grammar.
With 89 lexical categories, 19 lexical and morphological rules and 5 grammatical
rules, this grammar is able to successfully treat a significant range of linguistic phenomena. Moreover, due to the use of default inheritance hierarchies, the
categories are defined in a concise implementation that captures generalisations
shared by groups of categories. Subregularities and exceptions are also straightforwardly defined. A subset of the lexical category types defined in the grammar
is shown in Appendix A.
4.5
A Possible Universal Grammar
In this section, a possible formalisation of the theory of Universal Grammar (UG)
is described. The UG consists of principles and parameters, and the latter
are set according to the linguistic environment [Chomsky 1965], as discussed in
chapter 2. This proposal suggests that human languages follow a common set
of principles and differ among one another only in finitely many respects, represented by a finite number of parameters that can vary according to a finite
number of values.
In this work, UG is represented as a partially underspecified Unification-Based
Generalised Categorial Grammar, embedded in a default inheritance network of
types. The categories and rules are represented as types in the hierarchies and
encoded in terms of TDFSs, as described in the previous sections. The parameters
111
intrans-par
(
"PPP
((((
(
(
"
(
P
"
P
(
(
intrans-sent-par
trans-par
oblique-intrans-par
X
X
XX
XXX
X
ditrans-par
oblique-trans-par
Figure 4.104: Fragment of the Categorial Parameters Hierarchy
of the UG are formalised as types in the grammar also in terms of TDFSs, and
this allows the finite values they take to be specified as unset, as default, or as
non-default (absolute) values, as required.
The description of how the parameters are implemented in terms of a UBGCG starts with the encoding of the categorial parameters, which determine the
categories that are allowed for a particular language at a given time in learning. It
is followed by a description of word order parameters, which reflect the underlying
order in which constituents occur in a given language.
Categorial parameters define the categories allowed by the grammar at a
particular time during the learning process. Each of the categories in the grammar
has one categorial parameter associated with it and its value determines whether
the category is present in the grammar or not. If the parameter corresponding
to a particular category is active, then the category is allowed as part of the
grammar. Otherwise, if it is inactive, the category is not allowed. Then, if the
learner, which is discussed in chapter 6, detects that a given categorial parameter
is inactive, it does not include the corresponding category as part of its current
grammar. As a consequence, it is possible to determine different configurations
for the grammar, by activating different parameters, and different languages may
use different subsets of categories, as appropriate.
The 89 categorial parameters defined are grouped according to the syntactic
type of the categories they are associated with and ordered according to the
valence of these categories. The parameters of a given group are organised in
increasing order of complexity, reflecting the way the corresponding categories
are placed in the syntactic hierarchy, discussed in section 4.2.4. The higher the
valence of a category compared to the others with which it is grouped, the more
complex it is and the lower in the hierarchy it is placed. Figure 4.104 shows
the ordering of a fragment of the verbal categorial parameters, and table 4.1
shows the correspondence between these parameters and their categories. In
this hierarchy, intrans-par is the basic verbal parameter being associated with
intransitive verbs. If it is active, intransitive verbs are part of the grammar. As
transitive verbs are defined in terms of intransitive verbs, being more complex
in terms of valence than the latter, trans-par, the corresponding parameter, is
placed lower in the hierarchy than intrans-par.
In relation to the grammar, these parameters have the attribute ‘value’,
112
Table 4.1: Categorial Parameters
Parameters
Categories
intrans-par
intrans-sign (S\NP)
trans-par
trans-sign ((S/NP)\NP)
intrans-sent-par
intrans-sent-sign ((S/S)\NP)
oblique-intrans-par oblique-intrans-sign ((S/PP)\NP)
ditrans-par
ditrans-sign (((S/NP)/NP)\NP)
oblique-trans-par
oblique-trans-sign (((S/PP)/NP)\NP)
taking a boolean as value, which can be specified as either ‘true’ or ‘false’ (figure 4.105). In each of the categories in the grammar, the relevant categorial
parameter is defined with the morphosyntactic attributes (cat:m-feats), in the
attribute ‘allowed’ (figure 4.106 for the intransitive sign type). If allowed is
set as true, then the category is allowed in the grammar, but if it is set as false,
then the category is inactive and is not part of the grammar.




intrans-par


VALUE : /true
Figure 4.105: Specification of intrans-par Type
During the learning process, these parameters are activated, starting from
less complex to more complex, as the corresponding categories are required for
analysing sentences. Initially, as only some of the supertype categorial parameters
are active, with value:/true, the subtypes that are inactive override this value
with false, breaking the inheritance chain. As learning progresses and more
categories become active, the corresponding subtype categorial parameters are





























intrans-sign

RESULT:SIGN:CAT:M-FEATS
ACTIVE



: <!









: 






ALLOWED


: 
intrans-par
VALUE : /true
V2 : false
VFORM : /base
AUX : /false
INV : /false
SIGN : np-sign
DIRECTION :  subjdir
DIR-VALUE

:
backward


! >


Figure 4.106: Specification of intrans-sign Type
113





























also activated and consequently can inherit the value true from their supertypes.
Thus, as more categories become active, more categorial parameters inherit their
values by default from their supertypes, with the grammar becoming increasingly
more concise. For example, if trans-par is active and a ditransitive category is
necessary for analysing a sentence, its corresponding parameter, ditrans-par,
can only be activated if the supertype trans-par is active, since this is the
categorial parameter corresponding to transitive verbs and ditransitive verbs are
defined in terms of transitive verbs. However, a parameter can only be activated if
its supertype is active, but, if the latter is inactive, then the subtype has to remain
inactive too. Thus, if a ditransitive category is needed and neither ditrans-par
nor trans-par are active, then the former cannot be activated and the category
for ditransitive verbs is not allowed in the grammar. This means that ditransitive
verbs, being defined in terms of transitive verbs, can only become available in
the grammar after transitive verbs also are. As a consequence, categories become
available in the grammar in increasing order of complexity. Moreover, at any
given time, it is possible to know which categories are available by examining the
current parameter values.
In terms of learning, such an encoding of categorial parameters in the grammar allows for an account of the incremental nature of language acquisition, by
gradually activating these parameters from less complex to more complex. Thus,
given a specification of the categories that are initially allowed as part of the grammar, with the corresponding parameters being set as active (value:/true), all
the other categorial parameters are initialised as inactive (value:/false). Then,
as learning progresses, the parameters are gradually activated and increasingly
more complex categories are made available as part of the grammar.10
Word order parameters determine the underlying order in which constituents appear in a given language. For example, for English, an SVO language, these parameters specify that, in the canonical order, subjects appear to
the left of the verb, and objects to the right. On the other hand, they specify
that, for German, an SOV language, both the subject and the object appear to
the right of the verb [Croft 1992]. These parameters are based on the ideas proposed by Briscoe [1997 to 1999], taking into account typological considerations
[Comrie 1981], [Croft 1992].
There are 18 word order parameters defined and they are implemented as
types in a hierarchy. The supertype is gendir that specifies, by default, the
general direction for a language. Among its subtypes, we have subjdir that
specifies the direction of the subject, vargdir the direction of the other verbal
arguments, and ndir2 the direction of nominal categories. A fragment of the
parameters hierarchy can be seen in figure 4.107.
Word order parameters have one attribute, dir-value, that takes a value
10
Chapters 6 and 7 provide a more detailed explanation of the learning of these parameters,
looking at the construction of the categorial parameter hierarchy.
114
two-arg-sem
three-arg-sem
gendir
subjdir
ndir2 vargdir
detdir
ndir
Figure 4.107: Fragment of the Parameters Hierarchy
intrans-sign
intrans-raising-sign trans-sign oblique-intrans-sign intrans-equi-sign
oblique-trans-sign
ditrans-sign
trans-raising-sign
trans-equi-sign
Table 4.2: Types and Parameters
Sign
intransitive signs
transitive signs
oblique intransitive signs
intransitive with sentential complement signs
ditransitive signs
oblique transitive signs
115
Parameters
(subjdir = S\\NP)
(subjdir = (S/NP)\\NP)
(vargdir = (S//NP)\NP)
(subjdir = (S/PP)\\NP)
(vargdir = (S//PP)\NP)
(subjdir = (S/S)\\NP)
(vargdir = (S//S)\NP)
(subjdir = ((S/NP)/NP)\\NP)
(vargdir = ((S/NP)//NP)\NP)
(vargdir = ((S//NP)/NP)\NP)
(subjdir = ((S/PP)/NP)\\NP)
(vargdir = ((S/PP)//NP)\NP)
(vargdir = ((S//PP)/NP)\NP)
of type direction, which can be either backward or forward (figure 4.108).
Regarding the categories of the UB-GCG, word order parameters specify the
direction of each element in the subcategorisation list of a complex category. If
the parameter has value forward the subcategorised category is to be found to
the right and, if the value is backward, the category is to the left. This can be
seen in figure 4.106, for the intransitive sign, whose subject NP has direction set
as backward by the subjdir parameter. Table 4.2 shows the correspondence
between some of these parameters and some of the complex categories, where the
double slash indicates the position of the parameter in the category.
Moreover, since the parameters are organised in a default hierarchy, in the
absence of conflicting more specific values, they inherit their values by default
from their supertypes. For instance, in the case of English, the value of gendir
is defined, by default, as forward, capturing the fact that it is a predominantly
right-branching language (figure 4.108) and all its subtypes, like subjdir (figure
4.109) and vargdir (figure 4.110) inherit this default information. As the categories are also defined in terms of an inheritance hierarchy, the parameters and
their values in these categories are propagated throughout the hierarchy. Thus
subtypes inherit this information by default in the absence of the definition of
a more specific value. For example, an intransitive verb, which has the direction of the subject specified by subjdir (direction:subjdir), will be defined
as S/NP if subjdir has default value forward (figure 4.111). However, if as
in English the subject occurs to the left of the verb, utterances with the subject
to the left will trigger a change in subjdir to backward, which overrides the
default value, breaking the inheritance chain (figure 4.112). As a result, intransitive verbs are defined as S\NP, figure 4.106, for the grammar to account for
these sentences. In the syntactic dimension of this network, intransitive verbs
are considered the basic case of verbs and the information defined in this node
is propagated through the hierarchy to its subtypes, such as the transitive verbs.
This can be seen in figure 4.113, which shows the specification of the transitive
verb type, where vargdir defines the direction of the direct object. Figure 4.114
shows the transitive verb type expanded with the information that it inherits
from the intransitive verb type, including the direction of the subject, defined by
subjdir.



gendir
DIR-VALUE
:
/forward



Figure 4.108: Gendir Parameter
For the learner, the information about subjects (dir-value:/backward),
figure 4.112, has already been acquired while learning intransitive verbs, figure
4.106. Thus the learner does not need to learn it again for transitive verbs (figure
4.114) which not only inherit this information but also have the direction for the
116
subjdir
Figure 4.109: Subjdir Parameter
vargdir
Figure 4.110: Vargdir Parameter



subjdir
DIR-VALUE
:
/forward



Figure 4.111: Subjdir Parameter Expanded



subjdir
DIR-VALUE
:
/backward



Figure 4.112: Subjdir Parameter after Trigger








trans


RESULT:SIGN:CAT
: s





SIGN:CAT
:
np
! > 
ACTIVE : <! > , 

DIRECTION : vargdir

Figure 4.113: Interaction of the Transitive Verb Type with the Vargdir Parameter






















trans


RESULT:SIGN:CAT
: s
 




 SIGN:CAT : np

 

, 
ACTIVE : <! DIRECTION :  subjdir
 



DIR-VALUE : backward  





 SIGN:CAT : np








!>

 DIRECTION :  vargdir




DIR-VALUE : forward

Figure 4.114: Transitive Verb Type Expanded
object defined by vargdir (dir-value:/forward), figure 4.110.
Another parameter that is related to the canonical order of constituents in
different languages is the V2 parameter. This parameter regulates verb-second
phenomenon in main clauses. If it is activated, it allows the tensed verb to be
placed after the first constituent in main clauses. As a result, for a language like
German, which is SOV, V2 allows the verb to occur after the first constituent, resulting in orders like SVO, Adverb-VSO, and OVS ([Hyams 1986], [Roeper 1992]
117
































SOV-to-SVO-rule
NODE:CAT:ACTIVE






SIGN : np-subj-sign

,


DIRECTION:DIR-VALUE : backward






SIGN
:
np-obj-sign

>


DIRECTION:DIR-VALUE : forward





verb-cat




 RESULT:SIGN:CAT:M-FEATS:V2 : true








 ACTIVE : <  SIGN : np-subj-sign

1:NODE:CAT : 


DIRECTION:DIR-VALUE
: backward









SIGN
:
np-obj-sign


> 



DIRECTION:DIR-VALUE : backward
: <
Figure 4.115: SOV to SVO Rule
and [Kapur and Clark 1996]). If the parameter is inactive, this phenomenon is
not possible, as is the case for English. In terms of the categories in the grammar, this parameter is encoded in the v2 attribute as a verbal morphological
attribute with a boolean value (figure 4.106). If the parameter is activated, the
attribute has value true and the language allows the verb-second phenomenon,
which is generated using lexical rules. Otherwise, if the parameter is inactive,
the attribute has value false and this movement is not allowed in the language.
For example, let us assume that a lexical rule such as the putative rule shown in
figure 4.115 is used to change the canonical order of the constituents from SOV
to SVO. This rule is restricted to apply only to lexical signs whose V2 attribute
is set as true and that have SOV order, with the directions of both the subject
and the object set as backward. This is the case for German and the rule can be
successfully applied. However, such a rule could not be applied to a language such
as English, in which V2 is set to false and where the direction of the object is set
as forward. There may be many such rules to capture the movement of different
V2 constructions, in different V2 languages, and they are applied as appropriate
for a given language. For example, the rule shown in figure 4.115 could only be
applied to an SOV V2 language such as German because the direction of both
the subject and the object are required by this rule to be set as backward. In
this way, a language learner would have access to all such rules and these would
be selected as appropriate for each language.11
The UG has to be general enough to capture the grammar for any language.
Then, the parameters have to be set to account for a particular language, based
11
The question of the learning of lexical rules, investigating how the learner would learn which
rules are appropriate for a given language, is outside the scope of this work. This constitutes
a second stage in the learning process, when the learner has acquired enough information for
the patterns occurring in the lexicon to become apparent, building on the basis created by this
investigation for such a learning task. The learning of patterns in the lexicon is investigated by
Schütze [1995], however, he uses a different approach, employing data-intensive methods that
make it incompatible with this work.
118
on exposure to that language. Among these sentences, some will be triggers for
certain parameters, in the sense that some of the parameters will have to be set
to a certain values in order to capture these sentences, generating the appropriate
logical form. Thus, given a triggering sentence, some of the categorial parameters
may have to be set as true for the necessary categories to be available, and
for those available categories, some of the word order parameters may need to
have a specific value if the sentence is to be successfully analysed. In terms of
the learning process, having the parameters embedded in a default inheritance
hierarchy means that, even before a parameter is set by triggering data, it has
a value inherited by default from a supertype. This value will hold until the
occurrence of a trigger reinforces or disconfirms it. Furthermore, such an encoding
of the UG allows the definition of unset, default and non-default absolute values,
being compatible with many proposals in the language acquisition literature,
such as [Chomsky 1981], [Hyams 1986], and [Lightfoot 1991] among others, that
advocate that some parameters need to be initialised with default values, in the
beginning of the learning process.
The use of a default inheritance schema reduces the amount of information
to be acquired by the learner, since the information is structured and what is
learned is not a single isolated category, but a structure that represents a candidate category set. This is a clear and concise way of defining the UG with the
parameters being straightforwardly defined in the categories. It uses effectively
the default inheritance mechanism to propagate information about parameters
throughout the lexical inheritance network. This approach is well suited for a
Principles and Parameters Theory of UG, with very general grammar rules and
categories defined as types arranged in a default inheritance hierarchy which is
a kind of structure that is likely to have an important role in the way people organise many kinds of information, as pointed out by Sag and Wasow [1999]. For
a language learner, it is convenient to organise linguistic information in multiple
default inheritance hierarchies, since when learning new information, the learner
can use the existing hierarchies to classify the new information and needs only
to encode the minimum amount of arbitrary information.
4.6
The Annotated Sachs Corpus
The Principles and Parameters Theory suggests that children set the parameters
of the UG to a particular language, based on exposure to sentences provided by
their linguistic environment, spoken in a certain context. One of the ways in which
to approximate that is to use a corpus of utterances annotated with logical forms,
based on which parameters would be set to account for that specific language.
This section describes the particular corpus used in this work, as well as the
pre-processing and annotation required for the corpus to be used as the basis for
learning.
119
The corpus employed in this work is a subset of the Sachs corpus [Sachs 1983]
[MacWhinney 1995]. The Sachs corpus consists of Jacqueline Sachs’ naturalistic
longitudinal study of Naomi, her daughter, which contains spontaneous interactions between the child and her parents, phonemically transcribed, from the age
of 1 year and 1 month to 5 years and 1 month. This corpus contains a total of
29,814 sentences in English. From these sentences we extracted material for 2
different corpora: one with the parents’ sentences, containing 12,105 sentences
and the other with the child’s sentences, containing 17,709 sentences.
The use of the parents’ corpus as the basis for learning allows us to approximate the linguistic input that a child receives when learning her native language.
Moreover, by annotating this corpus with logical forms, it is possible to simulate
a part of the context a child has when listening to a sentence.
In order to annotate the parents’ corpus, it first needed to be pre-processed
to remove noise, phonological annotations, and some grammatical constructions
that are not relevant to this project. As this work concentrates on the investigation of verbal predicate argument structures, sentences such as 4.20 to 4.25
are not suitable for this study, being removed from the corpus to be annotated.
The original parents’ corpus contains 12,105 sentences, and the first stage of
pre-processing removed around 15% of the sentences containing noise. From the
remaining 10,292, a subset containing 4,650 sentences was selected from a period
ranging from when Naomi was 14 months to when she was 24 months of age.
These sentences went through a second stage of pre-processing and sentences
that contained only nominal constructions, interjections, elliptical constructions,
or that were incomplete were removed. From the 4,650 sentences, around 65%
were removed after the second stage of pre-processing, and the resulting corpus
to be annotated contained the remaining 1,517 sentences.
•
•
•
•
•
•
(4.20)
(4.21)
(4.22)
(4.23)
(4.24)
(4.25)
woofo woofo
baby birdie
and a cow says ...
yuck!
give me a kiss and I’ll get the xxx for you.
mmhm snow at the window huh?
After the pre-processing, the selected subset of the parents’ corpus was annotated with logical forms. The annotated Sachs corpus contains 1,517 sentences
with a wide variety of constructions, with for example, declarative, imperative
and interrogative sentences with rich verbal constructions, and unbounded dependencies, as can be seen in sentences 4.26 to 4.28, extracted from the corpus.
• (4.26) Are you done with looking at the pictures?
• (4.27) He is going to turn off the lights
120
• (4.28) Go in the kitchen and see Daddy
In order to annotate the parents’ corpus with the associated logical forms, a
UB-GCG for English that covers all the constructions in the corpus was built. 12
The parents’ corpus contains sentences annotated with logical forms, and an
example of the annotation can be seen in figure 4.116, for the sentence ‘I will
take him’, showing only some of the features for reasons of clarity. The logical
form associated with a sentence is constructed using the Sag and Wasow’s version
of MRS, as explained in section 4.2.2. Thus, each predicate in the semantics list
is associated with a word in the sentence, and, among other things, it contains
information about the identifier of the predicate (sit), the required arguments
(e.g. arg1 for the agent role and arg2 for the patient role, for the verb take), as
well as about the interaction among the predicates, specified by the boxed indices
in the argument roles.
































sign


ORTH : <!i, will, take, him ! >



CAT : s



MODE
: prop





INDEX
:
1
index


 
 







3
index
SIT
:
RELN
:
r-will

 
 

 
 
 RESTR : <!
 SIT : 1
,  PRON : i
,  


 
 

ARG1 : 2 index
NAMED : 4 index  
SEM : 






RELN : r-take   SIT : 6 index 






 



SIT
:
2






,
!
>




PRON
: him








ARG1
: 4




NAMED
: 5

ARG2 : 5 index

Figure 4.116: Sentence I will take him
The annotated sentences have a mean length of around 4.5 words, and from
the 6,893 words in the annotated corpus there are 706 different word forms being
used in these sentences. Apart from determiners, prepositions, and similar closed
class words, the most frequent categories occurring in these sentences are all
verbs, as can be seen in table 4.3. In relation to verbal constructions, verbs
occur 2,247 times in the corpus. Most of the main verbs are transitive verbs,
occurring approximately 24% of the time, while intransitive verbs occur only 7.7%
of the time. Sentences containing copula constructions are especially frequent,
accounting for 33% of the sentences. Unbounded dependencies occurred in 9%
of the sentences, with the vast majority of these cases being wh-questions with
object extractions, occurring in 7.5% of the sentences.
12
The characteristics of such a grammar, as well as a discussion of the constructions it covers,
are presented in the previous sections (4.1 to 4.4).
121
Table 4.3: Ten Most Frequent Open-Class Words
Word Frequency
is
553
are
159
do
157
want
108
can
64
doing
59
put
64
don’t
47
say
44
see
42
4.7
Summary
In this chapter, the implemented Unification-Based Generalised Categorial Grammar was described. It consists of categories and rules, implemented as types in
a default multiple inheritance hierarchy which contains information about orthographic, syntactic, semantic and linking constraints. Generalisations are encoded
in types higher up in a hierarchy and are propagated to their subtypes, while subregularities and exceptions are encoded by means of default specifications. As
a consequence, the resulting grammar captures concisely linguistic phenomena,
with different types of linguistic information being localised in different hierarchies, in an encoding that is easier to maintain and modify. With 89 lexical categories, 19 lexical and morphological rules and 5 grammatical rules, this grammar
is able to capture elegantly a wide variety of linguistic constructions, including
unbounded dependencies and coordinations.
This chapter also discussed how such an encoding is used to formalise a theory
of the Universal Grammar and associated parameters. They correspond to types
in the hierarchies, in an approach that provides a straightforward integration
of the parameters with the categories in the grammar. Moreover, the use of
default inheritance hierarchies allows information about the parameters to be
propagated from supertype to subtype, which is an important characteristic from
a learning perspective. In order to provide a linguistic environment for parameter
setting, a subset of the Sachs corpus, containing interactions between a child and
her parents, was annotated with logical forms. With this annotated corpus,
it is possible to simulate the environment in which a child acquires her native
language.
122
Chapter 5
Learning a Lexicon
In this chapter, two systems are described. The first one, the semantics learner,
attempts to learn the meanings of words from data. The second system, the
syntax learner, attempts to learn possible syntactic categories for the words in a
sentence so that a complete derivation is obtained. The semantics learner, was
implemented by Waldron [1999], based on an algorithm developed by Siskind
[1996], while the syntax learner was both developed and implemented by Waldron
[Waldron 1999 and 2000].
These two systems, as implemented by Waldron, are used to pre-process the
annotated Sachs corpus, assigning to each word in a sentence putative semantic
predicates and syntactic categories, which can be used as the basis for setting the
parameters of the UG. The descriptions provided in this chapter are based on
Waldron’s implementations, and concentrate especially on the semantics learner,
since it can be used on its own as the starting point for the investigation proposed
in this thesis. The syntax learner is only used for reasons of expediency, proposing putative syntactic categories for words in a sentence that result in possible
derivations.
5.1
Learning the Meanings of Words
Siskind [Siskind 1996] developed a computational model of lexical acquisition.
He investigated the learning of the mapping between words and logical forms
primarily from a computational perspective, but also related this task to that
faced by children when learning the meanings of words in their native language.
The algorithm he developed attempts to learn a lexicon containing for each
word an appropriate logical form, by analysing input sentences paired with possible meanings. The algorithm does not rely on the use of single word utterances
for the meaning of words to be unambiguously determined, or on prior access to
language specific information.
The use of sentence-meaning pairs relates to the problem of referential uncer123
tainty [Siskind 1993] that is faced by children who, when hearing an utterance,
may not be able to uniquely determine the meaning of the utterance from context. Thus, each sentence is paired with a set of possible meanings, among which
there is usually the correct one. However, the algorithm can also handle cases
where a sentence is paired with only incorrect meanings, which correspond to
noisy input, only requiring that utterances be non-noisy for a sufficient fraction
of the time. The algorithm also deals with polysemy, which is a lexical semantic
ambiguity where words may have more than one single meaning.
The learning process is regarded as a mapping problem, where a mapping from
words to meanings has to be learned, such that the meanings of words, when
combined, form the meanings of utterances containing those words. Semantic
interpretation is assumed to be compositional, with the meaning of an utterance
being composed of the meaning of each word in the utterance, and no information
can be added or deleted from the meanings of these words. As the lexicon learned
has each word mapped to a set of meanings denoting different senses for that
word, the meaning of an utterance is determined by choosing exactly one sense
for each word in that utterance.
For example, if the first sentence the learner receives is:
• (5.1) Mary lifted the block,
paired with the meaning:




















sem
RESTR

 

RELN : lift

SIT : 3 index  
SIT : 0 index ,  NAME

, 
 
ARG1 : 1 index   NAMED: Mary

: 1


ARG2 : 2 index


 




RELN
:
the
RELN
:
block

 



 


 SIT : 4 index ,  SIT : 5 index ! >


 


BV : 2
INST : 2





: <!



which can be represented in a linear form as:
{lift(
0
,
1
,
2
), mary(
3
,
1
), the(
4
,
2
), block(
5
,
2
)}
the learner is left with the task of finding out which word in the sentence maps
to which portion of the meaning of the sentence. The meaning of a sentence
is presented inside curly brackets, with predicates having their arguments represented inside brackets and separated by commas. For instance, in the logical form
associated with this sentence, lift( 0 , 1 , 2 ) has an event variable, 0 , and two
arguments, ‘ 1 ’ and ‘ 2 ’, where ‘ 1 ’ is coindexing the agent of ‘lift’ (in arg1) to
‘mary’, and 2 the undergoer of ‘lift’ (in arg2) to ‘the block’. The learner needs
124
to determine which of the predicates (lift( 0 , 1 , 2 ), mary( 3 , 1 ), the( 4 , 2 ) and
block( 5 , 2 )) to associate with each of the words in the sentence. For reasons of
clarity, the linear notation is used throughout this document, with event variables
not being explicitly represented unless otherwise required. Thus the logical form
associated with the sentence is represented as:
{lift(
1
,
2
), mary(
1
), the(
2
), block(
2
)}
The meaning paired with the sentence is decomposed into its component meanings
(predicates), where the bound variables, represented by indices such as 1 and
2 , are replaced by free variables, represented by a, b, ..., given the following
Decomposition Rule:
• In a predicate, every variable argument that is bound has its value replaced
by a free variable.
Applying the Decomposition Rule to the sentence Mary lifted the block, with
meaning {lift( 1 , 2 ), mary( 1 ), the( 2 ), block( 2 )}, results in {lift(a,b), mary(c),
the(d), block(e)} where the bound variable arguments in the logical form ( 1 ,
2 , ...) are replaced by free variables (a, b, ...). Each of these elements of the
meaning set can be associated with any of the words in the utterance, and thus
initially, the hypotheses the learner has are:
Mary1 : {lift(a,b), mary(c), the(d), block(e)}
lifted1 : {lift(a,b), mary(c), the(d), block(e)}
the1 : {lift(a,b), mary(c), the(d), block(e)}
block1 : {lift(a,b), mary(c), the(d), block(e)}
where each word sense in the lexicon is represented with a subscript number, and
has a set of possible hypothesised meanings, inside curly brackets, separated by
commas. Then, when hearing the utterance:
• (5.2) John lifted the ball,
paired with the meaning:
{lift(
1
,
2
), john(
1
), the(
2
), ball(
2
)}
which is decomposed into {lift(a,b), john(c), the(d), ball(e)}, the learner would
hypothesise that:
John1 : {lift(a,b) john(c), the(d) ball(e)}
lifted1 : {lift(a,b) john(c), the(d) ball(e)}
125
the1 : {lift(a,b) john(c), the(d) ball(e)}
ball1 : {lift(a,b) john(c), the(d) ball(e)}
This sentence contains two words that were seen before, and for which the learner
has already formulated hypotheses: the and lifted. By comparing the newly hypothesised meanings for lifted and the with the hypotheses created after the
previous utterance, the learner determines that two of the meaning elements for
these words are common between the two hypotheses:
lifted1 : {lift(a,b) john(c), the(d) ball(e)} ∩ {lift(a,b), mary(c), the(d), block(e)}
the1 : {lift(a,b) john(c), the(d) ball(e)} ∩ {lift(a,b), mary(c), the(d), block(e)}
The learner can then reduce the set of possible meanings for both lifted and the to:
lifted1 : {lift(a,b), the(c)}
the1 : {lift(a,b), the(c)}
In this case, the learner used common meaning elements across each occurrence
of a word, doing cross-situational inference to try to determine the meaning
of the word.
Informally, the learning system does not know the meaning of any word initially, so it implicitly hypothesises that each word can mean anything. Partial
knowledge of word meanings can allow the learner to filter out impossible hypothesised meanings of utterances that contain those words. Then, as sentences
are processed, the set of possible meanings for each word sense - which starts
as containing all possible meanings - is reduced until there is only one possible
meaning for each sense, which is when the word sense is determined. The intuition behind the algorithm is that the use of intersection in all the contexts in
which a particular word appears helps to determine the meaning of that word.
Thus a word cannot mean something that is not contained in the meaning of
an utterance containing that word. Such an approach uses two kinds of implicit
information: the different utterances in which a word appears, and the different
words appearing in an utterance. The learner assumes that words in an utterance
must contribute non-overlapping portions of the utterance meaning, adopting the
Principle of Exclusivity, which uses the knowledge about the meaning of some
words in an utterance to constrain the possible meanings of other words in the
same utterance.
When different senses of a word are used, problems will occur if the word
becomes inconsistent. A word is considered to be inconsistent when, for a given
sense, its meaning set becomes empty. This happens when an utterance is processed and a new sense for a word is used, because the intersection between the
possible meanings hypothesised for this new sense and another previously used
sense for the same word may not contain common elements. A sentence is consid126
ered to be inconsistent if any of its words is inconsistent. For example, assuming
that later on the learner is given the sentence:
• (5.3) These cars block this road
paired with the meaning:
{block(
1
,
2
), these(
1
), cars(
1
), this(
2
), road(
2
)}
the learner would hypothesise that:
these1 : {block(a,b), these(c), cars(d), this(e), road(f)}
cars1 : {block(a,b), these(c), cars(d), this(e), road(f)}
block1 : {block(a,b), these(c), cars(d), this(e), road(f)}
this1 : {block(a,b), these(c), cars(d), this(e), road(f)}
road1 : {block(a,b), these(c), cars(d), this(e), road(f)}
By intersecting the newly hypothesised meanings for block, with the hypotheses
created after the first utterance:
block1
= {block(a,b), these(c), cars(d), this(e), road(f)}
∩ {lift(a,b), mary(c), the(d), block(e)}
= {}
the result is the empty set.
A word that becomes inconsistent will affect the learning of other words, with
the learner not being able to reliably determine the meanings of these words, as
discussed in Siskind [1996]. In order to deal with this polysemy and to avoid
learning noisy meanings, the algorithm first performs a consistency test that
checks if, for a given sentence-meaning pair, inconsistencies will occur during
learning. If that is the case, the algorithm determines the minimum number
of word senses that need to be hypothesised for the utterance to be no longer
inconsistent and then processes the utterance as normal. Moreover, as each word
sense converges on meaning, it is assigned a confidence factor, which is initially
zero, but which is incremented every time it is used. The confidence factor collects
the evidence for each of the word senses, reducing the effects of noise which could
mislead the learner into converging to an incorrect meaning for a particular word
sense.
Let us assume that several words in the lexicon converged on meaning and
were assigned a confidence factor. Then, the following is a fragment of the cur-
127
rent lexicon, after the new sense of “block ”, block2 , is added:
block1 : {block(a)}, C=2
block2 : {block(a,b)}, C=0
he1 : {he(a)}, C=7
bought1 : {buy(a,b)}, C=4
the1 : {the(a)}, C=10
When, subsequently, a sentence like:
• (5.4) He bought the block
paired with the meaning:
{(buy(
1
,
2
), he(
1
), the(
2
), block(
2
)}
is given to the learner, as there are two distinct senses of block, the learner does
not know which one to use. As a consequence, it needs to consider the two
possibilities:
• He1 bought1 the1 block1 ,
whose meaning has as components:
{he(a), buy(b,c), the(d), block(e)}, and,
• He1 bought1 the1 block2 ,
whose meaning includes:
{he(a), buy(b,c), the(d), block(e,f)}
However, only the first one
He1 bought1 the1 block1 = {he(a), buy(b,c), the(d), block(e)},
contains all the necessary meaning components, and can be recomposed into:
{(buy(a,b) he(a) the(b) block(b)),
(buy(a,b) the(a) block(a) he(b),
(buy(a,b) the(a) he(a) block(b)),
(buy(a,b) block(a) the(b) he(b)),
(buy(a,b) he(a) the(c) block(c)),
128
(buy(a,b)
(buy(a,b)
(buy(a,b)
(buy(a,b)
(buy(a,b)
(buy(a,b)
(buy(a,b)
he(b) the(c) block(c)),
the(a) block(a) he(c)),
the(b) block(b) he(c)),
the(a) block(b) he (c),
block(a) the(b) he(c)),
block(a) he(b) the(c)),
he(c) the(d) block(e)), ... }
performing an operation that corresponds to a reverse application of the Decomposition Rule, instantiating the variables. In the resulting set of meanings, the
first element (buy(a,b) he(a) the(b) block(b)) is the desired sense assignment,
which corresponds to the meaning paired with the utterance. Having found the
sense assignment that is consistent with the meaning paired with the utterance,
the learner continues processing as usual.
The learner needs to consider all possible senses for the words in the utterance
being processed, aiming to find the combinations of sense assignments that are
compatible with the meaning paired with the utterance. In order to do so, the
learner verifies the consistency of each sense assignment in the cross product
of the senses of the words in the utterance (e.g. {He1 bought1 the1 block1 }
and {He1 bought1 the1 block2 }). If no consistent sense assignment is found,
then the smallest number of new meanings is incrementally added to the set of
possible senses for words in the utterance until the utterance becomes consistent.
Then, if there is exactly one consistent sense assignment as in this example,
the word senses contained in the sense assignment are used for processing the
sentence, and processing continues as normal. If there are more consistent sense
assignments, the best sense assignment is selected and processing continues as
normal. Given that each word sense is assigned a confidence factor corresponding
to the frequency with which this word sense is used after convergence, the best
sense assignment is defined as the one that has the highest overall confidence
factor, which is computed as the sum of the confidence factors for each word
sense used.
5.1.1
The Algorithm
In this section, the algorithm developed by Siskind [Siskind 1996] is described,
as implemented by Waldron [1999]. Waldron’s implemented algorithm differs
slightly from Siskind’s. The main difference between them is that Siskind differentiates between words with a null logical form (e.g. determiners and infinitivals)
and those with non-null logical form (e.g. nouns and verbs). Waldron considers
all the words to have a non-null semantics, providing a more uniform treatment
for all words.
The algorithm is on-line in the sense that each utterance is processed and
discarded before the next utterance can be processed, in a single pass of the
129
corpus, retaining only information about the mappings from words to senses.
These mappings are stored in three tables:
• Lsem (w ) - maps each word w to a set of senses.
• Psem (s) - maps each sense s to a set of meanings. Each sense is initially
mapped to any allowed meaning, and the algorithm monotonically removes
elements of Psem (s) until it is a singleton, which is when sense s converged.
When a sense converges, it is placed in Lsem (w ).
• Tsem (s) - maps each sense s to a confidence factor C, indicating the evidence
for the sense. The confidence factor of a sense is initially mapped to zero,
and gradually increases as the evidence for the sense increases. When the
temperature Tsem for a given sense s reaches a constant, µ, the sense freezes
and is considered to be learned.
Each sense passes through three stages, starting unconverged, converging on
meaning and being frozen. Different senses can be in different stages at a given
time. Senses that are not frozen, that is, whose confidence factor did not reach
the threshold µ, are subject to a garbage collection mechanism and removed from
consideration.
The algorithm used for learning word senses is ProcessUtterance:
Procedure ProcessUtterance(Utterance, Meaning)
Step 1 - If there is at least one consistent sense assignment {s1 ,..., sn } for
the utterance, choose the one with the highest confidence factor (computed as the
sum of the confidence factors of each word sense {Tsem (s1 ) + ... + Tsem (sn )} ),
and then execute Process({s1 , ..., sn }, Meaning).
This step verifies if there is at least one sense assignment that is consistent
with the meaning of the utterance, and after determining the one that has the
highest confidence factor, the algorithm processes the utterance.
Step 2 - Otherwise, find the smallest subset u’ ⊆ Utterance such that if a
unique sense is added to Psem (w) for each w ∈ u’, the utterance becomes consistent.
The second step finds the smallest number of new word senses that need to
be added to Psem (w ) to make the utterance consistent.
Step 2.1 - Add a new sense to Psem (w) for each w ∈ u’.
This step adds the new senses to the words that were determined to be necessary for the utterance to be consistent.
Step 2.2 - Go to Step 1.
130
After adding the necessary new senses, the algorithm returns to Step 1 to
process the utterance.
To determine the appropriate meaning for each word in the utterance, the
algorithm Process is used.
Procedure Process(Sense,Meaning)
Step 1 - For each word w in the utterance, remove from Psem (w ) any meanings that do not appear in the utterance meaning.
This step removes any meaning hypothesised as possible for a word that is
not part of the meaning of the utterance.
Step 2 - For each word w in the utterance, remove from Psem (w ) any meaning
that appears only once in the utterance meaning and is contributed by some other
word that has already converged on that meaning, also in the utterance.
For each converged word in the utterance this step checks if its meaning is
contained in the set Psem (w ) of possible meanings of other words in the utterance,
and if so, removes it from the latter.
Step 3 - For each word w in the utterance, increment the confidence factor
Tsem (w ) if the word sense has converged.
This step handles noise, minimising the effect of incorrectly converged senses.
The idea is that the learning system assumes that, by default, each word has
a single sense, and tries to build a lexicon that covers all the utterances in the
corpus. If the corpus has polysemy, some words have more than one sense. When
a new word sense occurs, the algorithm tries to map it to an existing sense, but
this leads to the existing sense becoming inconsistent if the two senses do not have
semantic elements in common. When this happens, the new sense is added to the
lexicon Psem (w ). Noisy utterances, not being paired with the correct meaning,
are treated as introducing new word senses, resulting in spurious senses being
created and added to Psem (w ). As these senses are unlikely to be encountered
again, they will not be sufficiently reinforced to become frozen, and will eventually
be discarded by the garbage collection mechanism.
As an example, supposing the algorithm is part-way through the learning process, and that the following is a fragment of the Psem lexicon:
John1 : {john(a), red(b), ball(c)}
took1 : {take(a,b), look(c,d)}
the1 : {the(a)}, C= 9
red1 : {red(a), ball(b)}
131
ball1 : {kim(a), ball(b)}
Then, the algorithm receives the utterance:
• (5.5) John took the red ball
paired with the following meaning:
{take(
1
,
2
), john(
1
), the(
2
), red(
2
), ball(
2
)}
By executing Step 1 of ProcessUtterance, the learning system finds that there
is a sense assignment of the words in the utterance that is consistent with the
meaning:
• John1 took1 the1 red1 ball1
The algorithm then executes Process(Sense, Meaning). In Step 1, the intersection between the set of meanings previously hypothesised and the ones newly
hypothesised results in:
John1
= {john(a), red(b), ball(c)} ∩ {john(a), red(b), ball(c), take(d,e), the(f)}
= {john(a), red(b), ball(c)}
since john(a) = john(a), red(b) = red(b), and ball(c) = ball(c)
took1
= {take(a,b), look(c,d)} ∩ {john(a), red(b), ball(c), take(d,e), the(f)}
= {take(a,b)}
since take(a,b) = take(d,e)
the1
= {the(a)} ∩ {john(a), red(b), ball(c), take(d,e), the(f)}
= {the(a)}
since the(a) = the(f)
red1
= {red(a), ball(b)} ∩ {john(a), red(b), ball(c), take(d,e), the(f)}
= {red(a), ball(b)}
since red(a) = red(b) and ball(b) = ball(c)
ball1
= {kim(a), ball(b)} ∩ {john(a), red(b), ball(c), take(d,e), the(f)}
= {ball(b)}
since ball(b) = ball(c)
with the resulting lexicon being:
132
John1 : {john(a), red(b), ball(c)}
took1 : {take(a,b)}
the1 : {the(a)}, C=9
red1 : {red(a), ball(b)}
ball1 : {ball(a)}
where the meanings of took and ball have converged. In Step 2, the algorithm
removes from the set of meanings of each of the words those meanings to which
other words have converged:
John1
took1
the1
red1
ball1
=
=
=
=
=
=
=
{john(a), red(b), ball(c)} - ({take(a,b)}, {the(a)} , {ball(a)})
{john(a), red(b)}
{take(a,b)}
{the(a)}
{red(a), ball(b)} - ({take(a,b)}, {the(a)} , {ball(a)})
{red(a)}
{ball(a)}
and the resulting lexicon is:
John1 : {john(a), red(b)}
took1 : {take(a,b)}
the1 : {the(a)}, C=9
red1 : {red(a)}
ball1 : {ball(a)}
with the meaning of red having converged also. After that, Step 3 is applied
and the confidence factors of the senses used for took, the, red and ball are incremented.
John1 : {john(a), red(b)}
took1 : {take(a,b)}, C=1
the1 : {the(a)}, C=10
red1 : {red(a)}, C=1
ball1 : {ball(a)}, C=1
In this example there was one sense assignment that was consistent with the
meaning associated with the utterance. Thus, no new senses needed to be added,
and the algorithm processes the utterance as normal.
In a second example the algorithm has to deal with polysemy, but all the
necessary word senses are already in the lexicon. Let us assume that the current
133
lexicon is:
John1 : {john(a)}, C= 9
saw1 : {hammer(a), wood-cutting-tool(b)}
saw2 : {see(a,b), go(c,d)}
had1 : {possess(a,b), want(c,d)}
had2 : {conduct(a,b), cause(c,d)}
Mary1 : {mary(a)}, C= 9
arrive1 : {arrive(a,b)}, C= 4
at1 : {at(a,b)}, C= 10
the1 : {the(a)}, C= 10
a1 : {a(a)}, C= 10
ball1 : {dance-party(a)}, C=4
ball2 : {toy(a)}, C=10
party1 : {political-organisation(a)}, C=4
This lexicon is polysemous, containing two senses for saw, had and ball. Then,
the algorithm receives the utterance:
• (5.6) John saw the ball
paired with the following meaning:
{see(
1
,
2
), john(
1
), the(
2
), dance-party(
2
)}
In Step1 of ProcessUtterance, the algorithm needs to analyse four sense assignments, as this utterance contains two polysemous words, each with two senses
in the lexicon:
• John1 saw1 the1 ball1 ,
• John1 saw1 the1 ball2 ,
• John1 saw2 the1 ball1 ,
• John1 saw2 the1 ball2 .
However, only one is consistent, containing all the semantic predicates needed to
obtain the meaning paired with the utterance:
• John1 saw2 the1 ball1
As this is the only consistent sense assignment, the algorithm proceeds executing Process((John1 saw2 the1 ball1 ) {see(a,b) john(a) the(b) dance-party(b)}),
134
which results in the following lexicon, where saw2 converged:
John1 : {john(a)}, C= 10
saw1 : {hammer(a), wood-cutting-tool(b)}
saw2 : {see(a,b)} C= 1
had1 : {possess(a,b), want(c,d)}
had2 : {conduct(a,b), cause(c,d)}
Mary1 : {Mary(a)}, C= 9
arrive1 : {arrive(a,b)}, C= 5
at1 : {at(a,b)}, C= 10
the1 : {the(a)}, C= 10
a1 : {a(a)}, C= 10
ball1 : {dance-party(a)}, C=5
ball2 : {toy(a)}, C=10
party1 : {political-organisation(a)}, C=4
In this next example, the algorithm has to deal with polysemy, but for a particular word in the utterance where none of the senses in the lexicon is the desired
one, and the algorithm has to add the new sense. If the algorithm receives the
utterance:
• (5.7) Mary had a party
paired with the following meaning:
{conduct(
1
,
2
), mary(
1
), a(
2
), celebration(
2
)}
where there is a polysemous word, had, with two senses. Step1 of ProcessUtterance finds that none of the sense assignments is consistent with the paired
meaning:
• Mary1 had1 a1 party1 ,
• Mary1 had2 a1 party1 .
In this case, Step 2 tries to find the smallest set of words in the utterance for
which a new sense has to be added to resolve the inconsistency. Adding a new
sense to party resolves that, and by executing Process((Mary1 had2 a1 party2 ),
{conduct(a,b) mary(a) a(b) celebration(b)}), party2 converges to celebration(a),
had2 converges to conduct(a,b), and the lexicon is updated to:
John1 : {john(a)}, C= 10
saw1 : {hammer(a), wood-cutting-tool(b)}
135
saw2 : {see(a,b)} C= 1
had1 : {possess(a,b), want(c,d)}
had2 : {conduct(a,b)}, C= 1
Mary1 : {mary(a)}, C= 10
arrive1 : {arrive(a,b)}, C= 5
at1 : {at(a,b)}, C= 10
the1 : {the(a)}, C= 10
a1 : {a(a)}, C= 10
ball1 : {dance-party(a)}, C=5
ball2 : {toy(a)}, C=10
party1 : {political-organisation(a)}, C=4
party2 : {celebration(a)}, C=1
In this case, the algorithm added a new sense to a word already in the lexicon.
5.1.2
Evaluation of the Semantics Learner
The system implemented by Waldron [Waldron 2000] learns a lexicon that maps
words to semantics, while dealing with noise and polysemy. Waldron’s algorithm
is used to pre-process the annotated corpus, assigning a logical form to each
word in a sentence, as discussed in chapter 6. In this section, an evaluation of its
performance is discussed.
Waldron’s semantics learner was tested on the annotated Sachs corpus, containing 1,517 parents’ sentences paired with logical forms, as described in section
4.6. This corpus was given as input to the semantics learner, which analysed
each sentence and logical form pair in turn, trying to determine an appropriate
mapping between words and logical forms. Thus for each word in a sentence, the
learner tried to determine the appropriate logical form according to the algorithm
described in the previous sections. If the learner could determine a putative semantic predicate for every word in a sentence, then these predicates were returned
as result. Otherwise, if a predicate could not be determined for every word in a
sentence, no result was returned. From the 1,517 sentences, the learner returned
a putative word-logical form mapping for 63.6% of the corpus, with 95.23% of the
results returned being correct, and the remaining 4.55% containing at least one
incorrect predicate. Most of the incorrect mappings were due to the very frequent
co-occurrence of some words in only a particular context, which meant that the
learner could not use cross-situational inference to distinguish them. This is the
case of the control verb want and the infinitival to, in sentences like Do you want
to eat?. As they occur very often together, the learner could not reliably distinguish them and assigned want the logical form for to and vice-versa. Otherwise,
the semantics learner has a good performance, assigning correct logical forms for
95.23% of the sentences that it successfully processes.
136
5.2
Learning the Syntactic Category of Words
By using the closely linked syntax and semantics in CGs, Waldron developed and
implemented an algorithm to learn the mapping between a semantic predicate
and a syntactic category. From the mapping between a word and its semantics,
the algorithm tries to infer the syntactic category associated with the word. The
algorithm is partly algebraic, and tries to construct derivations, given the current
knowledge that it has about the syntactic categories and semantic predicates of
the words in the utterance. The algorithm regards categories in their atomic
formulation, ignoring feature structure information, and it assumes that the syntactic category of nouns, names, pronouns and particles are known. Another
assumption made is that the algorithm knows whether an utterance is imperative, interrogative or declarative, since this information is sometimes necessary in
order to construct the derivation of an utterance. To construct derivations, the
algorithm uses generalised weak permutation, forward application, backward application, forward composition and backward composition, and the set of lexical
rules described in chapter 4.
Initially, the algorithm starts with knowledge only about nouns, names, pronouns and particles, and the predicates associated with the words of a sentence.
Then, by applying the grammatical rules and some heuristics, the algorithm tries
to obtain possible derivations. Each application of a rule or heuristic is assigned
a weight (or confidence factor) and each derivation is assigned a weight computed
by multiplying the weights used to generate it. Sometimes alternative derivations
can be generated, resulting in different applications of rules or heuristics, each
derivation having an associated weight. For example, if the algorithm receives as
input the sentence:
• (5.8) I see Bill,
paired with the semantics:
{ i(
1
), see(
1
,
2
), bill(
2
)}
and the current lexicon is:
i1 : {i(a)}, NP
bill1 : {bill(a)}, NP
the algorithm tries to determine the appropriate categories for each word in the
utterance that allows the learner to produce a successful derivation. It generates
an initial hypothesis, using the current state of knowledge:
137
I
i(a)
NP
see
Bill
see(b,c) bill(d)
?
NP
where the words in the sentence are in the first line, the corresponding semantic
predicates in the second, and the syntactic categories in the third. After determining all words in the utterance for which the syntactic categories are known,
the algorithm has to infer the categories for the remaining words, in this case see,
so that the derivation ends in S:
I
i(a)
NP
see
Bill
see(b,c) bill(d)
?
NP
S
Therefore, with NP ? NP the algorithm has to generate a derivation that results
in S:
NP ? NP = S
NP+?+NP = S
where ‘+’ is a variable over the slash operators. Then, using the grammatical
rules defined, the algorithm generates further hypotheses. Among the possible
categories that can be inferred from NP+?+NP=S, which can also be written as
?= S+NP+NP, there are:
?=
?=
?=
?=
S/NP/NP,
S\NP\NP,
S/NP\NP, and
S\NP/NP
with the latter two being able to generate a derivation resulting in S, when combined with the other categories. By using generalised weak permutation, these
two are considered equivalent by the syntax learner, which does not make any
use of the thematic roles in the undecomposed logical form ({i( 1 ) see( 1 , 2 )
bill( 2 )}), choosing only one of them:
NP S\NP/NP NP = S
As the category for see is inferred, the resulting lexicon is updated to:
i1 : {i(a)}, NP
138
see1 : {see(a,b)}, S\NP/NP
bill1 : {bill(a)}, NP
This is a simple case where the category for only one word in the utterance
has to be inferred. However, more complex cases can arise, with categories having
to be inferred for several words, and with different possibilities for each word. In
these cases, the algorithm may not be able to establish uniquely the appropriate
category for each word sense, keeping all the possibilities inferred, each with an
appropriate confidence factor. Eventually, if the word sense appears in enough
different syntactic contexts, one of the possibilities gains enough evidence to have
a significantly higher confidence factor than the others, which is when the word
sense converges to that category.
For example, in the case of the sentence:
• (5.9) The big dog slept
with logical form:
{the(
1
), big(
1
), dog(
1
), sleep(
1
)}
assuming that the categories for the words the, big, dog are known, only the category for slept, with meaning sleep(d), has to be inferred:
The
big
dog
slept
the(a) big(b) dog(c) sleep(d)
NP/N N/N
N
?
S
Among the possibilities for the category for sleep(d), the following ones are all
consistent with NP/N N/N N ? = S:
• ?= S\(NP/N)\(N/N)\N,
• ?= S\(NP/N)\N, and
• ?= S\NP
As there is no way for the algorithm to determine which one should be used
based on the information available, all of these putative categories are considered
valid hypotheses. Then, they are stored with their confidence factors, and the
algorithm waits for more utterances that can disambiguate them.
For each utterance, the algorithm keeps alternating between applying grammatical rules, trying to infer categories and substituting the newly inferred categories in the derivation, until nothing more can be done. At this stage, if the
139
algorithm succeeds in inferring categories for all the words in the utterance, all
possible derivations for the utterance are generated. However, there are occasions where the algorithm is unable to generate a complete derivation. When
this happens, it may be because the algorithm needs to infer the categories of
several words in the utterance, and the current state of knowledge is insufficient
to account for the word senses used. Even if the algorithm cannot generate a successful derivation, it may be able to combine some of the constituents together
into fragments of a derivation. In this case, the algorithm keeps track of the
fragments that were generated, with corresponding weights, since these can be
potentially useful in the processing of subsequent utterances.
5.2.1
The Algorithm
In this section, a formalisation of the algorithm developed by Waldron
[Waldron 1999] is described. This algorithm is also on-line, and after analysing a
sentence it retains only information about the mappings from senses to syntactic
categories. These mappings are also stored in three tables:
• Lsyn (ws) - the syntactic lexicon, which maps each word-sense pair, ws, to
an appropriate syntactic category c.
• Psyn (ws) - for each possible word-sense pair, ws, this table stores a set of possible categories c. Each word-sense pair is initially mapped to any allowed
category, and the algorithm monotonically removes elements of Psyn (ws)
until it is a singleton, which is when the category c converged, and can be
placed in Lsyn (ws).
• Tsyn (c) - maps each putative category c, associated to a word-sense pair,
to a confidence factor, Csyn , that indicates the evidence for the category.
A putative category is initially mapped to zero, but as evidence for this
hypothesis is provided its confidence factor increases. A constant µsyn indicates the freezing point, and a putative category c becomes frozen when
Tsyn (c) ≥ µsyn .
Each possible category starts unconverged, and as the evidence for it increases,
so does its confidence factor. When the confidence factor of a hypothesis c reaches
the freezing point, µsyn , the hypothesis is selected as the appropriate category for
the word-sense pair ws. Putative categories that are not frozen and that have a
low confidence factor are subject to a garbage collection mechanism.
The algorithm used to learn syntactic categories is ProcessSenseAssignment. It receives as input an utterance and associated meaning, and the wordsense mapping for each word in the utterance. During the processing of an
utterance, the algorithm updates each of the three tables as necessary.
140
Procedure ProcessSenseAssignment(Utterance, Meaning, Mapping)
Step 1 - Find if there is at least one possible syntactic category assignment
{c1 , ..., cn } for the utterance, which produces a successful derivation.
This step verifies if there is at least one putative category assignment that
results in a successful derivation.
Step 1.1 - For each putative category c which contributes to a successful
derivation of the utterance, increment the confidence factor Tsyn (c).
Step 1.1 reinforces those putative categories that can be used in a successful
derivation.
Step 2 - Otherwise, create new putative categories for a subset ws’ ⊆ Wordsense pairs, such that when the new categories are added to Psyn (c) for each c ∈
ws’, one or more successful derivations for the sentence are produced.
This step creates new putative categories to try to find successful derivations
for the sentence.
Step 2.1 - Add the newly created putative categories to Psyn (c) for each c ∈
ws’.
This step adds to the lexicon Psyn the new putative categories to the wordsense pairs that were determined to be necessary for producing successful derivations.
Step 2.2 - Go to Step 1.
Step 3 - If no complete derivations were obtained, ignore this utterance.
If no derivations could be produced, the algorithm stops processing the current utterance.
In the following example, the algorithm is part-way through the learning process, and has the following hypotheses:
bill1 : NP, Csyn = 100
mary1 : NP, Csyn = 100
john1 : NP, Csyn = 100
block1 : NP, Csyn = 100
block2 : S\NP/NP, Csyn = 3
likes1 : S\NP/NP, Csyn = 10
sees1 : S\NP/NP, Csyn = 7
when it receives the utterance:
• (5.10) Bill likes Mary,
141
paired with the semantics:
{like(
1
,
2
), bill(
1
), mary(
2
)},
where Bill is paired with sense bill1 , which corresponds to the predicate bill(a);
Mary is paired with sense mary1 , which corresponds to the predicate mary(a),
and likes is paired with sense likes1 , which corresponds to the predicate like(a,b).
In Step 1, the algorithm tries to determine a possible category assignment that
allows for a successful derivation of the utterance. It generates an initial hypothesis, using the current state of knowledge:
Bill
bill(a)
bill1
NP
NP
likes
Mary
likes(b,c) mary(d)
likes1
mary1
S\NP/NP NP
S\NP
S
As this category assignment produces a derivation, the confidence factors of each
of the categories used is updated, following Step 1.1:
bill1 : NP, Csyn = 100
mary1 : NP, Csyn = 100
john1 : NP, Csyn = 100
block1 : NP, Csyn = 100
block2 : S\NP/NP, Csyn = 3
likes1 : S\NP/NP, Csyn = 11
sees1 : S\NP/NP, Csyn = 7
In this case only the confidence factor of likes was updated, because the categories
of both Bill and Mary, being names, are known by the learner, and assigned a
high confidence factor, which makes them frozen.
The algorithm in this first example has all the necessary categories to provide
a successful derivation that is consistent with the word-senses used. Let us consider now that the next sentence the algorithm receives is:
• (5.11) Mary runs
paired with meaning:
{run(
1
), mary(
1
)},
142
where Mary is paired with sense mary1 , which corresponds to the semantic predicate mary(a), and runs is paired with sense run1 , which corresponds to the
predicate run(a). In Step 1 the algorithm determines that there are no possible category assignments that generate a derivation given the current state of
knowledge, and it proceeds to Step 2. The algorithm then determines that it
can generate the following derivation fragment:
Mary
mary(a)
NP
runs
run(b)
?
where the category for run1 has to be found. The algorithm then determines that
a successful derivation can be obtained if S\NP is added as a possible category
for run1 :
Mary
mary(a)
NP
NP
runs
run(b)
?
S\NP
S
Step 2.1 adds this hypothesis to the lexicon:
bill1 : NP, Csyn = 100
mary1 : NP, Csyn = 100
john1 : NP, Csyn = 100
block1 : NP, Csyn = 100
block2 : S\NP/NP, Csyn = 3
likes1 : S\NP/NP, Csyn = 11
sees1 : S\NP/NP, Csyn = 7
run1 : S\NP, Csyn = 0
Step 2.2 returns the execution to Step 1, which now can find a successful derivation, and as a result in Step 1.1 the confidence factors are updated:
bill1 : NP, Csyn = 100
mary1 : NP, Csyn = 100
john1 : NP, Csyn = 100
block1 : NP, Csyn = 100
block2 : S\NP/NP, Csyn = 3
likes1 : S\NP/NP, Csyn = 11
143
sees1 : S\NP/NP, Csyn = 7
run1 : S\NP, Csyn = 1
In this example the algorithm cannot find a successful derivation for the sentence given the current state of knowledge, and has to add a new entry to the
lexicon containing a putative category for the sense run1 .
5.2.2
Evaluation of the Syntax Learner
The syntax learner was evaluated using the annotated Sachs corpus. The corpus
contains 1,517 sentences which were annotated using a grammar where 89 distinct
lexical categories capture the constructions found in the corpus. The words in the
lexicon exemplify these lexical categories defined. Each utterance is first analysed
by the semantics learner, and if the semantics of each word in the utterance can
be determined, then the syntax learner is activated. Thus every sentence in
the corpus, for which an appropriate mapping between words and logical forms
could be determined, was given as input to the syntax learner, as well as a
lexicon containing for each word sense the associated logical form, and when
available, its putative syntactic categories. Initially, the lexicon contains only the
syntactic category for nouns, names, pronouns and particles, but, as the syntactic
categories of words corresponding to other semantic predicates are determined,
they are also added to the lexical entries. As the semantics learner returned a
result for 965 sentences out of the 1,517, the syntax learner is evaluated in terms of
these. For each sentence given as input, the syntax learner attempted to return a
mapping between the word-logical form pairs in a sentence and putative syntactic
categories in a way that produced a complete derivation. If the syntax learner
could find a putative category for each word-logical form pair in a sentence that
produced a derivation, it returned the derivation as result. For many sentences
there was more than one possible category assignment for each word and logical
form pair that produced a derivation, and when this was the case, the learner
returned all possible category assignments. On the other hand, if there was at
least one word-logical form pair in the sentence for which the learner could not
find a category, then no result was returned. The space of possible categories
contains all the atomic categories S, NP, N, PP and PRT, and all the complex
categories that can be generated from them.
When the syntax learner was tested in this unrestricted search space, in a
typical run, from the 965 input sentences, putative category assignments were
returned for 52.6% of the sentences. However, from these 508 sentences that
received putative category assignments, only 4.7% had the correct category assignment for every word in the sentence. For the remaining 95.3%, the putative
category assignments returned contained at least one incorrect mapping between
word-logical form and syntactic category. The incorrectly hypothesised categories
usually contained a large number of arguments, and were too complex, with sev144
eral levels of embeddings. For example one of the categories hypothesised for
red in red ball is (((((S\NP)\(NP/N))\((S/NP)/NP))/N)/NP), instead of N/N.
In this unrestricted search space, the syntax learner does not perform well. The
putative syntactic categories are too complex and long, and do not correspond
to linguistic intuitions. For example, one of the possible categories hypothesised
for an auxiliary verb like are in are they eating, is the category NP/NP, instead
of the more conventional (S\NP)/(S\NP). This overgeneration is a significant
problem if the output of the syntax learner is to be used as a basis for setting
the parameters of the UG. However, as is discussed in chapter 6, the principles
and parameters learner analyses this output and only derivations containing categories permitted by the UG are considered for setting the parameters, with all
the others being discarded.
5.3
Summary
In this chapter, two systems were discussed and evaluated. The first, the semantics learner, attempts to learn the mapping between words and meanings and
to build a lexicon containing the meaning associated with each word sense. The
second system, the syntax learner, tries to learn possible syntactic categories for a
word sense using an algebraic approach. In this work they are used to pre-process
the annotated Sachs corpus, but there is a significant problem of overgeneration,
and they are only able to assign correct semantic and syntactic categories for a
small portion of the corpus. Therefore, some mechanisms discussed in chapters 6
and 7 have to be used to deal with this problem. Moreover, the output produced
by these systems does not contain any information about the linking between
the semantic arguments and syntactic complements of the categories, and this is
something that that needs to be learned, as discussed in section 7.1.
145
Chapter 6
The Learning System
The aim of this work is to investigate the process of grammatical acquisition
from data. For this purpose, a computational learning system was implemented,
which is composed of a Universal Grammar with its principles and parameters,
and a learning module. This system receives input from a corpus annotated with
logical forms, and this data is used to fix the values of the parameters of the
UG to the particular language expressed in the corpus, following the Principles
and Parameters Theory. The UG, as described in section 4.5, is implemented
as a UB-GCG embedded in a default inheritance network of lexical types. The
learner is exposed to an environment provided by the annotated Sachs corpus
(section 4.6) that simulates the environment to which a child is exposed. In
this environment the learner may have to deal with noise and ambiguity. The
learner needs to be able to overcome these problems if it is to converge to the
language of the environment. To guide the learner in this convergence, a Bayesian
interpretation of the learning process is used. At the end of the acquisition
process, the performance of the learner is evaluated by comparing the parameter
settings of the UG with those of the target grammar, for the learning tasks
performed. The grammar defined in chapter 4 is considered to be the target to
which the learner has to converge, with respect to the learning aspects being
investigated.1 This framework can serve as a basis for the investigation of several
aspects of language acquisition.
In this chapter the learning system is described, starting with an explanation
of the architecture of the learning system (section 6.1), followed by a description
of the learning approach employed (section 6.2), and its implementation (section
6.2.1).
1
In this work we concentrate on the learning of subcategorisation frames and word order
information. This builds the basis for a second stage of learning, such as the acquisition of lexical
rules, which is when the learner has enough information for the generalisations occurring in the
lexicon to become apparent, and this second learning phase is not addressed in this work. The
learning of lexical rules is investigated by Schütze [1995], but he uses data intensive methods
that are not compatible with this work.
146
6.1
Architecture of the Learning System
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6)
7/. 3. 445
6)
7/. 89
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Figure 6.1: Architecture of the Learning System
The learning system is equipped with a UG with its principles and parameters,
and a learning module that, given the input data, sets the parameters of the UG
to the language exemplified in this input. This process is shown in figure 6.1.
The input data consists of sentences annotated with logical forms that are
pre-processed by the semantics and the syntax learners, described in chapter 5.
They are combined together to try to determine semantic and syntactic category
assignments for each of the words in a sentence. For example, given the sentence:
• (6.1) Do you see a cup
147
paired with the logical form:




















sem
RESTR




RELN : see



RELN : do
  SIT : 2


 



SIT : 1 index ,  ARG1 : 3 index ,




ARG1 : 2 index


ARG2
: 4 index








5
index
SIT
:
6
index
SIT
:
7
index
SIT
:









 RELN : a
 NAME : cup
! > 
 NAME : you






NAMED : 3
BV : 4
NAMED : 4





: <!


whose corresponding linear notation is:
{do(
1
,
2
), see(
2
,
3
,
4
), you(
5
,
3
), a(
6
,
4
) , cup(
7
,
4
)}
the semantics learner determines semantic assignments for each word in the sentence:
{do1 =do(a,b), you1 =you(c,d), see1 =see(e,f,g), a1 =a(h,i), cup1 =cup(j,k)}
The syntax learner determines, among others, the following syntactic assignments
for each of the words:
{(do1 =(NP/NP), you1 =NP, see1 =S\NP/NP, a1 =NP/N, cup1 =N ),
(do1 =(S\NP)/(S\NP), you1 =NP, see1 =S\NP/NP, a1 =NP/N, cup1 =N )}
If the semantics and syntax learners are successful in determining possible
semantic and syntactic category assignments for the sentence, these assignments
are evaluated by the valid category assignment detection module. In order
to check if there is at least one valid category assignment (VCA) for the sentence
this module uses two principles [from Steedman 2000]:
• the Principle of Lexical Head Government assumes that the responsibility
for specifying both bounded and unbounded dependencies lies in the lexical
specification of the syntactic type of the head of these dependencies, and
• the Principle of Categorial Type Transparency states that, for any language,
the semantic interpretation together with a number of language-specific
directional parameter settings uniquely determines the syntactic category
of a word.
The idea is that, in CGs, lexical entries for words are responsible for specifying (bounded and unbounded) dependencies, containing the mapping between
words and their semantic interpretations. From the semantic interpretation of
148
a word and some directional information for a language, it is possible to determine the syntactic form of the corresponding category. For instance, in English
an intransitive verb, such as run, is a verbal one-place predicate from an entity
(the subject) to a proposition, where the subject occurs to the left of the verb,
and the verb is syntactically realised as S\NP. Thus, in this work, we assume
that these principles, that we refer to as Categorial Principles, determine how
the semantic predicate of a word is syntactically realised. These principles are
closely related to the Projection Principle [Chomsky 1981] that states that the
selectional requirements of a word are projected onto every level of syntactic
representation, and to the Extended Projection Principle [Chomsky 1982] that
also requires that all sentences have a subject. The task executed by the VCA
detection module is necessary because the syntax learner returns every possible
assignment for the words in a sentence that results in complete derivations, given
the space of possible categories. Thus, this module searches for VCAs, where a
category assignment is considered to be valid if it not only provides a complete
derivation for the sentence, but also has each word in the sentence paired with
a syntactic category that is appropriate for the associated semantic predicate,
according to the Categorial Principles. All other assignments are discarded. For
example, in the syntactic category assignments for sentence 6.1, because do is a
verb, with verbal predication, it is not compatible with category NP/NP which
has nominal predication. Thus, only the second assignment is a VCA and can
subsequently be used to set the parameters of the UG.
If there is a consistent category assignment for each word in the sentence, the
trigger detection and processing module checks which triggers the sentence
provides. As discussed in chapter 2, the notion of triggers varies in the literature.
In the scope of this work, a triggering sentence is a sentence paired with a logical
form, with corresponding valid semantic and syntactic assignments, which provide evidence for one or more parameters. Moreover, a particular trigger does not
necessarily provide evidence for a change in the current settings of a parameter,
but can also give favourable evidence for keeping this setting. A sentence can
provide triggers for several parameters, depending on the constructions it contains. For instance, sentence 6.1 contains a transitive verb (see) that provides,
among other triggers, those for the direction of the subject and of the object in
relation to the verb. This module also extracts frequency information about the
words in the sentence and the associated semantic and syntactic predicates. The
learner may need to know the frequency with which a word is associated with
a particular semantic predicate and a given syntactic category for some of the
learning tasks.
Triggers that are detected are used by the parameter setting module to
set the parameters of the UG.
This same process is repeated for each sentence in the corpus, with the learning
system using information about the words, the semantic predicates, the syntactic
categories and other triggers expressed in the sentence, for the learning tasks. All
149
these activities are performed by the algorithm Process-Input(Corpus).
Procedure Process-Input(Corpus)
Step 1 - Read Sentence S from corpus with logical form LF
Given an input corpus, this step reads a sentence-logical form pair.
Step 2 - Find a semantic assignment Sem for each word in sentence S, based
on the logical form LF, by executing ProcessUtterance(S,LF).
In this step the semantics learner receives a sentence and logical form pair as
input and tries to determine a semantic assignment for each word in the sentence.
Step 2.1 - If Sem = {} Go to Step 1.
If the semantics learner could not find an assignment, the sentence is ignored,
and the learner returns to Step 1 to process the next sentence.
Step 3 - Find syntactic assignments Syn for each word in sentence S,
given its semantic assignment in Sem, by executing ProcessSenseAssignment(S,LF,Sem).
If the semantics learner returned assignments for the words in the sentence,
these are given as input to the syntax learner, together with the sentence and
logical form. The syntax learner tries to determine all the syntactic assignments
for the words in the sentence that result in derivations that span through the
whole sentence.
Step 3.1 - If Syn = {} Go to Step 1.
If the syntax learner could not find possible assignments, the sentence is ignored, and the learner returns to Step 1 to process the next sentence.
Step 4 - For each semantic predicate in Sem, from Syn determine Synvalid ,
the syntactic assignment that is valid according to the Categorial Principles.
The VCA detection module, in this step, establishes if there is a valid syntactic
category assignment for every word in the sentence, given all the assignments
returned, by evaluating each syntactic assignment according to the Categorial
Principles. Those assignments that are not considered valid are discarded.
Step 4.1 - If Synvalid = {} Go to Step 1.
If there is no valid category assignment the sentence is ignored, and the learner
returns to Step 1 to process the next sentence.
Step 5 - Determine set of triggers T expressed in sentence S, logical form
LF, semantic assignment Sem and syntactic assignment Synvalid .
This step determines the triggers expressed in the sentence. Following Dresher
and Kaye [1990], we assume that the learner knows how to detect triggers in a
triggering sentence, and that it also knows which parameter is being expressed
150
in a given trigger. In this way, the trigger detection module analyses a sentencelogical form pair, searching for triggers that can set the values of the parameters.
Step 5.1 - Store frequency information about each word w, its semantic assignment Semw , and its syntactic assignment Synw .
The learner stores frequency information about the words in the sentence and
their occurrence with particular semantic and syntactic assignments.
Step 6 - Use the triggers in T to set the parameters of the UG, by executing
Process-Triggers(S,T).
The triggers found are processed and used to set the parameters of the UG.
Step 7 - Go to Step 1.
The learner goes back to Step 1 to process the next sentence.
As an example, consider that the learner is given the sentence:
• (6.2) Bill likes Beth
paired with the logical form
{like(
1
,
2
,
3
), bill(
4
,
2
), beth(
5
3
)}.
After Step 1 reads this sentence and logical form pair, these are given as input
to the semantics learner in Step 2, where the following semantic assignments for
each word in the sentence are returned:
Sem = {like1 =like(a,b,c), bill1 =bill(d,e), beth1 =beth(f,g)}
In Step 3, the syntax learner receives these as input and determines that the
following is one assignment that provides a possible derivation for the sentence:
Syn = {(like1 =(S/NP)\NP, bill1 =NP, beth1 =NP)}
Step 4 determines that this syntactic assignment in Syn is valid for the semantic predicates in Sem, according to the Categorial Principles.2 The algorithm
2
In this simplified example, Step 4 is straightforwardly applied. If, however, the sentence
was Mary likes the red ball, with logical form and putative assignments shown below, the learner
would have to analyse each possible assignment, determine that only the first assignment is
valid, and discard all the others:
Sem = {like( 1 , 2 ), mary( 1 ), the( 2 ), red( 2 ), ball( 2 )}
Syn = {(like1 =(S/NP)\NP, mary1 =NP, the1 =NP/N, red1 =N/N, ball1 =N),
...
(like1 =NP\NP,
mary1 =NP,
the1 =((S\NP)/((((S\NP)\(NP/N))\((S/NP)/NP))/N)),
151
then determines, in Step 5, the triggers expressed in the sentence: T = {NP,
NP, S/NP\NP}. Step 5.1 stores frequency information about each word and
corresponding category assignments, in this case: like1 = {like(a,b), S/NP\NP
}, bill1 = {bill(c), NP} and beth1 = {beth(d), NP}. Step 6 gives the triggers
as input to Process-Triggers that sets the parameters of the UG, and Step 7
goes back to Step 1 to process the next sentence.
This is the algorithm that controls the learning process. It calls the procedures ProcessUtterance and ProcessSenseAssignment, already described
in sections 5.1.1 and 5.2.1 respectively, and Process-Triggers, that is explained
in section 6.2.1.
At the end of the learning process when the learner has received all the sentences in the corpus, the performance of the learner is evaluated. This evaluation
is related to the state of the parameter settings of the UG in relation to the target
grammar, as discussed in chapter 7 .
6.2
Bayesian Incremental Parameter Setting
The acquisition process uses a Bayesian interpretation of the learning problem,
which guides the learner in the parameter setting task. The Bayesian Incremental
Parameter Setting (BIPS) algorithm, defined by Briscoe [1999], determines how
the learner is to proceed when faced with triggers for the parameters, given
the current parameter settings. Some of the triggers will reinforce the current
settings, while others will negate them, and the learner may have to change some
of the current parameter values. As the parameters are embedded in a default
inheritance network, the learning algorithm changes the parameter settings in
constrained ways according to the positions of the parameters in the hierarchy,
from subtypes to supertypes. As many of the changes to the parameters will result
in more than one possible grammar reflecting the current parameter settings, the
learner has to choose one among these grammars. For example, the fragment of
hierarchies shown in figures 6.2 to 6.4 are all compatible with subjdir set to
backward, and vargdir, detdir and ndir set to forward. In these figures ‘/’
corresponds to forward and ‘\’ to backward. Subtypes that do not adopt the
value inherited by default from the supertype, break the inheritance chain, and
specify their own values, as is the case of vargdir in figure 6.2. The problem
for the learner is to decide which possible option is more appropriate, given the
goal of converging to the target. One criterion (bias) to help the learner in this
decision is to prefer compact grammars whenever possible, using a Minimum
Description Length (MDL) style bias [Rissanen 1989].
The MDL Principle states that the best hypothesis to infer from the data is the
one which does not make too many errors in relation to the data seen, and at the
same time can be described concisely. In terms of grammars, this can be thought
red1 =(((((S\NP)\(NP/N))\((S/NP)/NP))/N)/NP), ball1 =NP)}.
152
gendir = \
ndir2 = /
ndir
vargdir = /
subjdir
detdir
gendir = \
ndir2
vargdir = /
ndir = /
subjdir
detdir = /
gendir = /
Figure 6.2: Word Order Parameters - Hierarchy 1
ndir2
ndir
vargdir
subjdir = \
detdir
gendir = \
ndir2 = /
ndir
vargdir = /
subjdir
detdir
Figure 6.3: Word Order Parameters - Hierarchy 2
gendir = \
ndir2
vargdir = /
ndir = /
subjdir
detdir = /
gendir = /
ndir2
ndir
vargdir
subjdir = \
detdir
Figure 6.4: Word Order Parameters - Hierarchy 3
gendir = \
ndir2 = /
ndir
vargdir = /
153
detdir
gendir = \
subjdir
of as selecting the grammar that not only covers the input triggers, but is also
concisely described. In this way, the most probable grammar is that consistent
with the parameter settings and where the default inheritance hierarchy has the
maximum number of parameters that inherit their value by default, and the
minimum number of parameters that override this default and need to explicitly
specify a value.
Thus, assuming that what the learner is looking for is a grammar that captures
well the input sentences and that is compact, the learner uses a Bayesian (MDLstyle) interpretation of the learning process to evaluate the changes being made
to the grammar during the setting of the parameters. In the formalisation of
the BIPS algorithm [from Briscoe 1999] the most probable grammar g in the
grammar space G, given the set of triggers T seen so far is:
p(g ∈ G | T ) =
p(g)p(T | g)
p(T )
(6.1)
where:
• the prior probability of a grammar, p(g), in this interpretation represents the
compactness of a particular grammar, in terms of the number of attributevalue specifications that need to be explicitly defined,
• the likelihood probability, p(T | g), expresses how well the grammar represents the triggering input,
• the probability of the data, p(T ), is a constant factor among all the hypotheses, and can be ignored, and
• the posterior probability, p(g | T ), represents the combination of the prior
and likelihood probabilities.
In effect, the most probable grammar is computed as:
g = argmaxg∈G p(g)p(T | g)
(6.2)
The prior probability of a grammar is based on its compactness and this measure
is used to order the space of possible grammars: the more compact the grammar,
the higher its prior is. The compactness of a grammar is measured in terms of the
amount of information that needs to be explicitly defined. Each of the grammars
is defined in terms of a hierarchy (denoted by CON (T ype, ⊆)) where its categories
are types. Each type is encoded as a set of attribute-value specifications (AVSs),
and each of the AVSs has a probability associated:
• a non-default (absolute) specification, corresponding to a principle, has
probability 1 (p(AV Si = abs) = 1),
154
• a categorial parameter has probability 1,
• a word order parameter can be set to either forward (AVSi =forward) or
backward (AVSi =backward), or it can be left unset (AVSi =?), and each
of these settings has a probability associated, such that the sum of the
probabilities of these values must be 1:
p(AV Si = backward) + p(AV Si = f orward) + p(AV Si =?) = 1,
A parameter that has not yet been set by triggers (an unset parameter)
has a probability of 0.5 (p(AV Si =?) = 0.5) for the unset value and a
probability of 0.25 for each of the two other values.
After a parameter is set, the unset value has probability 0 and then the
probability is distributed as appropriate between the other two values:
p(AV Si = backward) + p(AV Si = f orward) = 1,
The prior probability of a category c is defined as the product of the probabilities
of the AVSs that are explicitly defined in the category, normalised with respect
to the entire category set in UG:
Q
AV S∈CON (c,⊆) p(AV S)
Q
p(c) = P
(6.3)
c∈CON (T ype,⊆)
AV S∈CON (c,⊆) p(AV S)
where the probability of each AVS is assumed to be independent. In relation to
a particular grammar, the prior probability of a category is defined by restricting
the normalisation to the grammar:
Q
AV S∈CON (c,⊆) p(AV S)
p(c | g) = P Q
(6.4)
c∈g
AV S∈CON (c,⊆) p(AV S)
The prior probability of the grammar is the product of the probabilities of all
AVSs explicitly defined in the grammar:
Y
p(g ∈ G) =
p(AV S)
(6.5)
AV S∈CON (T ype,⊆)
where CON (T ype, ⊆) defines the inheritance network, denoting a minimal set of
feature structures representing the category set for a given grammar. The grammar space contains the grammars allowed by the UG that have the principles in
common and vary in relation to the setting of their parameters. These grammars
155
are in effect differentiated in terms of the product of the probabilities of the default and absolute parameter specifications defined. Following these constraints
the prior probabilities of the grammars are assigned to ensure that:
X
p(G) =
p(g) = 1
(6.6)
g∈G
This gives a higher prior to those grammars where the number of explicitly defined
AVSs is lower, making a more efficient use of the inheritance hierarchy to define
and propagate information through the grammar.
The likelihood probability is obtained by computing the amount of triggering
data, T, generated by the target grammar that a particular grammar is able to
model. It is defined as the product of the probabilities of each input trigger t:
Y
p(T | g) =
p(t | g)
(6.7)
t∈T
The probability of a triggering sentence is defined as the product of the probabilities of the categories assigned to it, its valid category assignment (VCA):
Y
p(t | g) =
p(c | g)
(6.8)
c∈V CA(t)
This gives a preference for grammars that can account with high probability
for the triggering data. In these grammars the parameter settings are at least
partially compatible with the target, given the triggers seen so far.
Using this interpretation of the learning problem, the most probable grammar
is the one consistent with the parameter settings and where the default inheritance hierarchy is the most concise. This grammar has the maximum number
of parameters that inherit their value by default, and the minimum number of
parameters that override this default.
6.2.1
The Implemented Learning Algorithm
In this section we describe an implementation of the BIPS algorithm as an on-line
incremental algorithm which uses the triggers detected in the input data to set
and update the parameter values [Villavicencio 2000a, 2000c and 2000d].
The learning system receives as input a sentence annotated with the appropriate logical form, a semantic assignment, and a set of putative syntactic assignments. The learning system analyses the category assignments and gets those
that are valid according to the UG. These are processed by the trigger detection
module which determines if there are triggers for any of the parameters. The parameter setting module uses these triggers to reinforce the appropriate parameter
values, as formalised by the procedure Process-Triggers.
156
There are two classes of parameters: categorial parameters and word order
parameters, and they are treated slightly differently by the learning algorithm.
Categorial parameters, as explained in section 4.5, determine which categories
are allowed as part of the grammar. These parameters are encoded in each of
the categories and are binary-valued. If they are set as true, the corresponding
categories are part of the UG, but if they are set as false the categories are not
part of the grammar. The grammar space contains all the possible grammars
that contain the five basic categories S, NP, N, PP and PRT, and we assume that
the grammars have complex categories containing at most 5 arguments, since
this seems to be the maximum arity observed in a language such as English. We
further assume that the definition of the rules and categories are predefined in
the UG, but that their corresponding categorial parameters must be set as true
for them to become available. Initially the UG is only partially specified, with
only the parameters of some of the categories set as true, which means that the
learner has to use a restricted set of categories to process the sentences. However,
as the learner is exposed to more complex categories, the parameters for these
categories are also set as true. If a categorial parameter associated with a given
category type is true, when a trigger containing that category is processed the
triggers provided by the sentence can be used to set the word order parameters.
On the other hand, if the parameter is false when a sentence containing that
category type is processed, and the supertype of the category is true, then the
appropriate categorial parameter is set to true, and the triggers provided by
the category are used as evidence for other parameters. A third case is when
the subtype is false and its supertype is also false, which results in the triggers
provided for the sentence being ignored, since the categories required to parse
the sentence are not yet part of the learner’s grammar. The algorithm used to
set these parameters is Process-Triggers. It receives as input a sentence and
the triggers that are expressed in this sentence, that were detected by the trigger
detection module, as described in Step 5 of the Process-Input procedure.
Procedure Process-Triggers(S,T)
Step 1 - For all triggers ti in the set of triggers T, expressed in sentence S,
determine the subset of parameters Pract from the set of parameters Pr that is
activated by the triggers
This step finds all the parameters that are activated by the triggers that are
present in the current sentence.
Step 2 - Determine the subset of parameters Prcat from Pract that are Categorial Parameters.
This step determines all the categorial parameters for which there are triggers
in the sentence, where the categorial parameters determine which categories are
currently part of the grammar, as discussed in section 4.5.
157
Step 2.1 - If all parameters in Prcat have value=true, then determine the
subset of parameters Prwo from the set of parameters Pract that are word order
parameters and the subset Two , with the triggers from T that are triggers for word
order parameters, and execute Reinforce-Parameters(Two ,Prwo ).
If all the categorial parameters in P rcat have their corresponding categories as
part of the grammar, i.e., are set as true, then the learner has all the categories
that are required to process the sentence as part of its current grammar. In this
way, it can continue processing the remaining triggers.
Step 3 - Otherwise, determine the subset of parameters Prf alse from Prcat
that have value=false.
If there are categorial parameters for which there are triggers in the sentence,
but whose categories are not yet part of the grammar, determine these parameters.
Step 3.1 - Determine the subset of parameters Prs from the set of parameters
Pr, which are optimal supertypes for the parameters in Prf alse , such that when
the corresponding categories are added to the grammar, the resulting grammar is
the most concise.
For these categorial parameters that are not part of the grammar, the algorithm determines suitable supertypes such that the addition of the corresponding
categories to the grammar requires the minimum number of AVSs to be explicitly
encoded in the grammar.
Step 3.2 - If all the parameters in Prs have value=true, then set the categorial parameters in Prf alse to value=true.
This step determines if all the supertypes of the categorial parameters have the
corresponding category as part of the grammar, and then activates the categorial
parameters in Prf alse , making their corresponding categories also part of the
grammar.
Step 3.3 - Determine the subset of parameters Prwo from the set of parameters
Pract that are not categorial parameters, and the subset Two , with the triggers
from T that are not triggers for categorial parameters, and execute ReinforceParameters(Two ,Prwo ).
Then the remaining triggers are processed for those parameters for which
there are triggers in the sentence, but that are not categorial parameters.
Step 4 - Otherwise ignore triggers in T for parameters in Pract .
If there is any supertype parameter from P rs that is set as false, then the
learning algorithm ignores the sentence.
As an example, continuing the execution in the previous example, in Step
1, the learner identifies that NP is a trigger for np-par=true, S/NP\NP
for trans-par=true, subjdir=backward and vargdir=forward, and NP for
np-par=true, resulting in the set {np-par=true, trans-par=true, sub158
jdir=backward, vargdir=forward}. In Step 2 the learner determines that
the set of categorial parameters Prcat is {np-par, trans-par}, and in Step 2.1
it verifies if these categorial parameters are set as true. This is the case for
np-par, the categorial parameter associated with the basic category NP. However, trans-par, the parameter associated with the transitive verb category, is
set as false and is not yet part of the grammar, so the learner has to execute
Step 3, where it determines that the set of parameters Prf alse that are set as
false is {trans-par}. Thus, transitive verbs have to be added to the grammar.
In the case of the transitive verb category, there are several different possible
insertion places, as shown in figures 6.5, 6.6 and 6.7, in some fragments of
possible hierarchies. In these hierarchies the categories are shown in an atomic
formulation for reasons of clarity, but they are defined in terms of feature structures. In these figures the specifications that need to be explicitly encoded are
represented in bold font, and those specifications that are inherited are in normal font. As can be seen, some of these hierarchies are more compact then
others, making more effective use of the inheritance mechanism. For instance,
the one shown in figure 6.5 is the most compact while that in figure 6.7 is
flatter, and much less concise. One assumption made in order to find the most
concise encoding for the grammar is that the learner uses Light’s [1993] algorithm. This algorithm determines the optimal insertion place in the hierarchy
for a new type and its required attributes. The optimal place is computed as
the one where the minimum number of parent types can provide the maximum
number of required attributes by inheritance, while blocking the minimum number of attributes from being inherited, because of conflicting values. In Step
3.1 the learner determines that an optimal supertype for trans-par is intranspar, which is the parameter associated with the intransitive verb category, with
Prs ={intrans-par}. In this way, the most concise grammar results from the
addition of trans-par as a subtype of intrans-par and of the corresponding category, the transitive verb category, as a subtype of the intransitive verb category,
which corresponds to the hierarchy shown in figure 6.5. Due to the use of default inheritance hierarchy, all the information about the transitive verb category
(S|NP|NP), shown in figure 6.8, that is already contained in the intransitive verb
category (S|NP), in figure 6.9, is inherited by the former. This encoding requires
the minimum number of AVSs to be explicitly added to the grammar, as shown
in figure 6.10. The learner then determines in Step 3.2 if intrans-par is set as
true. As this is the case, the learner defines trans-par as a subtype of intranspar and sets the former to true, which makes the corresponding category part
of the grammar. In Step 3.3 the learner proceeds by executing ReinforceParameters({S/NP\NP}, {subjdir=backward, vargdir=forward}).
At any given moment it is possible to determine the grammar the learner has
by checking which categorial parameters are set as true.
Before defining the second algorithm, Reinforce-Parameters, we now consider the second class of parameter: the word order parameters. These parameters
159
Figure 6.5: Possible Hierarchy 1
Figure 6.6: Possible Hierarchy 2
)+*+,
%("#$"#$ %
! "#$
! "%
#$
#
&' "#$ &' "#
& "#
Figure 6.7: Possible Hierarchy 3
160
$$
'' "#$
$- )



















trans
RESULT:SIGN:CAT

CAT-TYPE : s-cat
M-FEATS:ALLOWED


ACTIVE : <! SIGN:CAT : np
DIRECTION : subjdir,


 SIGN:CAT : np
! >
DIRECTION : vargdir

: 

:
trans-par


















Figure 6.8: Transitive Verb Type Partially Expanded












intrans
RESULT:SIGN:CAT
ACTIVE
:

CAT-TYPE : s-cat
M-FEATS:ALLOWED


SIGN:CAT : np
/! >
<!
DIRECTION : subjdir
: 

:
intrans-par
Figure 6.9: Specification of Intransitive Verb Type








trans

RESULT:SIGN:CAT:M-FEATS:ALLOWED
: trans-par 





SIGN:CAT
:
np

/! >
ACTIVE : <! > , 

DIRECTION : vargdir

Figure 6.10: Specification of Transitive Verb Type
161











gendir
subjdir
ndir2 vargdir
detdir
ndir
Figure 6.11: Fragment of the Parameters Hierarchy
intrans-sign
specify the direction of each element in the subcategorisation list of a complex
category,
as describedtrans-sign
in section
4.5. These
parameters are binary-valued and
intrans-raising-sign
oblique-intrans-sign
intrans-equi-sign
can be set as backward or forward, defining if a subcategorised element is to
be found
to the left or to the right, respectively.
They are defined in a hieraroblique-trans-sign ditrans-sign trans-raising-sign
trans-equi-sign
chical relationship, with the supertype being gendir, which specifies, by default,
the general direction for a language and from which all the other parameters
inherit. Among the subtypes we have subjdir, which specifies the direction of
the subject, vargdir, the direction of the other verbal arguments and ndir2, the
direction of nominal categories. A fragment of the parameters hierarchy can be
seen in figure 4.107, repeated here as figure 6.11. As the categories are defined
in terms of an inheritance hierarchy, the parameters (and their values) in these
categories are propagated throughout the hierarchy, from supertypes to subtypes,
which inherit this information by default.
For the word order parameters, the learning algorithm stores frequency information: each of the word order parameters has a prior and a posterior probability
associated with each of its values, and a current setting which corresponds to the
value with the highest posterior probability. Following Briscoe [1999], the probabilities associated with the word order parameter values correspond to weights
which are represented in terms of fractions, with the denominator storing the
total evidence for a parameter and the numerator storing the evidence for a particular value of that parameter. For instance, if the value backward of the
subjdir parameter has a weight of 9/10, it means that 9 out of 10 triggers for
subjdir provided evidence for the value backward, and only 1 out of 10 for the
other value, forward. Table 6.1 shows a possible initialisation for the subjdir
parameter, where the prior has a weight of 1/10 for forward, corresponding to
a probability of 0.1, and a weight of 9/10 for backward, corresponding to a
probability of 0.9.
An approximation is used for computing the posterior probability associated
with each parameter, where the incremental computation of the likelihood probability is smoothed with the prior probability, as we now explain. Initially, in the
learning process the posterior probabilities associated with each parameter are
initialised to the corresponding prior probabilities. These probabilities are going
to define the parameter settings initially used, with the learner setting a parameter to the value with the highest posterior probability. For instance, in table 6.1,
162
as backward has a higher posterior probability, it is used as the initial current
value for the parameter. Then, as triggering sentences are successfully parsed,
the posterior probabilities of the parameter settings that allowed the sentence
to be parsed are reinforced. The evidence provided by the trigger of a certain
parameter is represented as an addition to the denominator and/or numerator
of each of the posterior weights of the parameter values. In this case, when a
sentence provides evidence for one of the settings of a parameter the denominator of the posterior probabilities of the two values are incremented by 1, and the
numerator of the value being reinforced is also incremented by 1. For example,
if the triggers provide evidence for backward, and its current posterior is 9/10,
it is updated to 10/11, while the posterior probability of forward is updated to
1/11. Table 6.2 shows the status of the parameter after 5 triggers that provided
evidence for the value backward. The learner uses the evidence provided by the
triggers to choose certain parameter values, in order to be able to parse these
triggers successfully while generating the appropriate logical form. Further triggers are used to reinforce these values or to negate them, and the learner sets the
parameters to the values with the highest posterior probabilities. This approach
ensures that a trigger does not cause an immediate change to a different grammar. Instead, the learner has to wait for enough evidence in the data before it
can change the value of any parameter. As a consequence, the learner behaves in
a more conservative way, being also robust to noise present in the input data, as
discussed in chapter 7.
Table 6.1: Initialisation of a Parameter
Value
Forward
Prior
Posterior
Prob. Weight Prob. Weight
1
1
0.1
0.1
10
10
Backward
0.9
9
10
0.9
9
10
The values of a subtype (leaf) word order parameter are determined by the
direct evidence provided by the triggers, as is the case of subjdir and vargdir.
On the other hand, a supertype (non-leaf) parameter such as gendir, receives
only indirect evidence from its subtypes and its posterior probabilities are set according to the posterior probabilities of the subtypes that inherit its current value
by default. As the parameters are defined in a default inheritance hierarchy, each
time the posterior probabilities of a given parameter are updated it is necessary
to update the posterior probabilities of its supertypes and examine the hierarchy
to determine what the most probable grammar for these settings is, given the
goal of converging to the target. This has to be done because many changes in
163
the parameters can result in more than one possible grammar, as shown in figures
6.2 to 6.4.
As the learner has a bias towards a concise grammar, by requiring that the
supertype parameter is set to the current value used by the majority of its subtypes, it is possible to ensure that the grammar will have the minimum number
of explicitly defined AVSs. In this way, as the values of the subtypes are being
set, they influence the value of the supertypes. If the value of a given subtype
differs from the value of the supertype, the subtype overrides the inherited default value and breaks the inheritance chain. As a result, this subtype does not
contribute to the posterior probability of the supertype. For instance, in figure
6.4, subjdir overrides the default value specified by gendir, breaking the inheritance chain. Unset subtype parameters inherit, by default, the current value of
their supertypes, and while they are unset they also do not influence the posterior
probabilities of their supertypes.
The algorithm used to set these parameters is Reinforce-Parameters. It
receives a set of triggers and the corresponding set of parameters as input.
Procedure Reinforce-Parameters(Two ,Prwo )
Step 1 - For each parameter pri ∈ Prwo , get values v1 and v2 , associated with
pri , with probabilities pv1 and pv2 .
This step gets the corresponding values and probabilities for the parameters
which had triggers in the sentence, and that are not categorial parameters.
Step 2 - For corresponding trigger ti ∈ Two with value vi , if vi is equal to v1 ,
set the probability of v1 , pv1 , to:
pv1 =
numerator(v1 ) + 1
denominator(v1 ) + 1
(6.9)
and set the probability of v2 , pv2 , to:
Table 6.2: Status of a Parameter
Value
Forward
Prior
Posterior
Prob. Weight Prob. Weight
1
1
0.1
0.07
10
15
Backward
0.9
9
10
164
0.93
14
15
pv2 =
numerator(v2 )
denominator(v2 ) + 1
(6.10)
If the value being reinforced by the trigger ti , is equal to v1 , then the posterior
probability of v1 is reinforced by adding 1 to both the numerator and denominator of the corresponding fraction. Numerator(x) is a function that returns the
numerator of a fraction, and denominator(x) returns the denominator of a fraction. Moreover, the second value v2 has its denominator incremented by 1 also.
Step 3 - Otherwise if vi is equal to v2 , set the probability pv1 to:
pv1 =
numerator(v1 )
denominator(v1 ) + 1
(6.11)
and set the probability pv2 to:
pv2 =
numerator(v2 ) + 1
.
denominator(v2 ) + 1
(6.12)
Otherwise, the learner reinforces the posterior probability of v2 , by adding 1
to both the denominator and numerator of the corresponding fraction, and by
adding 1 to the denominator of v1 .
Step 4 - If pv1 > pv2 , set the current value vc in parameter pri to v1 and the
probability pvc to pv1 .
If v1 is the value with the highest posterior probability in parameter pri , set
the current value vc of this parameter to v1 , and the probability pvc to pv1 .
Step 5 - Otherwise, if pv2 > pv1 , set the current value vc of parameter pri to
v2 and the probability pvc to pv2 .
Otherwise set the current value vc of this parameter to v2 , and the probability
pvc to pv2 .
Step 6 - Execute Compute-Probabilities-of-Supertypes for the word order parameters, which determines the most concise encoding that reflects the parameter settings.
After the parameter settings were reinforced, it is necessary to examine the
current hierarchy and determine appropriate settings for the supertype parameters so that the most concise encoding for the grammar is obtained.
If the learner continues executing the previous example, ReinforceParameters({S/NP\NP}, {subjdir=backward, vargdir=forward}), in
Step 1 the learner determines that subjdir has values v1 =forward, with probability pf orward =1/48 and value v2 =backward, with probability pbackward =47/48.
165
These values are reinforced in Step 3, with vi =backward, as expressed in
the trigger, and providing evidence for v2 , whose probability is updated to
pbackward =48/49 and v1 (forward) has its probability updated to pf orward =1/49.
Step 5 is executed, with posterior probability of backward being greater than
that of forward, and the current value of subjdir being set to backward.
This same process is executed for reinforcing the value forward for the parameter vargdir as the trigger provides evidence for v1 , where pf orward =33/35
and pbackward =2/35. Step 2 updates its probability to pf orward =34/36 and the
probability of v2 to pbackward =2/36. After all the parameters in P rwo were processed, the algorithm then proceeds by executing Compute-Probabilities-ofSupertypes for the current settings of the UG.
Procedure Compute-Probabilities-of-Supertypes
Step 1 - For each supertype word order parameter prsi in the set of parameters
Pr find the set of subtype parameters prwov1 in Pr that have v1 as current value,
and the set of subtype parameters prwov2 in Pr that have v2 as current value.
The goal of this step is to find all the subtypes of a given supertype, and
divide them in two groups according to the value they adopt as current.
Step 2 - If |prwov1 | > |prwov2 | then set the current value of the supertype
prsi to v1 .
This step is executed if the majority of the subtypes adopted v1 as current
value, and sets the current value of the supertype also to v1 .
Step 2.1 - Then set the posterior probabilities pprsi of the supertype parameter
prsi according to the posterior probabilities of all the subtypes that adopted v 1 as
current value:
P
prj ∈prwov1 pprj (v1 )
pprsi (v1 ) =
(6.13)
| prwov1 |
P
prj ∈prwov1 pprj (v2 )
pprsi (v2 ) =
(6.14)
| prwov1 |
This step sets the value of the posterior probabilities of the supertype to the
normalised sum of the posterior probabilities of the subtypes that adopted v1 as
current value.
Step 3 - Otherwise if |prwov2 | > |prwov1 | then set the current value of the
supertype prsi to v2 .
If the majority of the subtypes adopted value v2 as current value, then the
current value of the supertype is also set to v2 .
Step 3.1 - Then set the posterior probabilities pprsi of the parameter prsi from
the posterior probabilities of all the subtypes that adopted v2 as current value:
166
pprsi (v1 ) =
P
pprsi (v2 ) =
P
prj ∈prwov2
pprj (v1 )
| prwov2 |
prj ∈prwov2
pprj (v2 )
| prwov2 |
(6.15)
(6.16)
The posterior probabilities of the supertype are set based on the posterior
probabilities of all the subtypes that adopted v2 as current value.
Step
4 - Else if (|prwo
| = |prwov2 |) and
P
P v1
pr ∈prwo
pprj (v1 )
pr ∈prwo
pprj (v2 )
v2
j
( j |prwov1v1 |
>
)
|prwov2 |
then set the current value of the supertype prsi to v1 .
If there is an equal number of subtype parameters that adopt each of the
values as current values, the learner compares the normalised sum of the posterior
probabilities of the current value in each of the cases. If the sum of the posterior
probabilities of the set of subtypes whose current value is v1 is the highest, then
v1 is set as the current value adopted by the supertype.
Step 4.1 - And set the posterior probabilities pprsi of the parameter prsi from
the posterior probabilities of all the subtypes that adopted v1 as current value:
P
prj ∈prwov1 pprj (v1 )
(6.17)
pprsi (v1 ) =
| prwov1 |
P
prj ∈prwov1 pprj (v2 )
pprsi (v2 ) =
(6.18)
| prwov1 |
The posterior probabilities of the supertype are set to the normalised sum of
the posterior probabilities of the subtypes that adopted v1 as current value.
Step
5 - Otherwise ifP(|prwov1 | = |prwov2 |) and
P
pr ∈prwo
pprj (v2 )
pr ∈prwo
pprj (v1 )
v1
j
>
)
( j |prwov2v2 |
|prwov1 |
then set the current value of the supertype prsi to v2 .
This step is executed if there is an equal number of subtype parameters that
adopt each of the values as current value and the sum of the posterior probabilities
of the subtypes whose current value is v2 is the highest. Then v2 is set as the
current value adopted by the supertype.
Step 5.1 - Set the posterior probabilities pprsi of the parameter prsi based on
the sum of the posterior probabilities of all the subtypes that adopted v 2 as current
value:
P
prj ∈prwov2 pprj (v1 )
pprsi (v1 ) =
(6.19)
| prwov2 |
167
pprsi (v2 ) =
P
prj ∈prwov2
pprj (v2 )
| prwov2 |
(6.20)
The posterior probabilities of the supertype are set to the normalised sum of
the posterior probabilities of the subtypes that adopted v2 as current value.
Step
6 - Else if (|prwo
| = |prwov1 |) and
P
P v2
pr ∈prwo
pprj (v2 )
pr ∈prwo
pprj (v1 )
v1
j
( j |prwov2v2 |
=
)
|prwov1 |
then set the posterior probabilities pprsi of the parameter prsi to 0.5.
If the number of subtypes that adopt each of the values as current value is the
same, and the normalised sum of the posterior probabilities of the subtypes in
each of these cases is the same, then set the posterior probability of the supertype
to 0.5.
"$"%*#$+,
&%%'(%)
"!!#!$
&%%'(%)
-.0/1( 2
Figure 6.12: Word Order Parameter - Hierarchy 4
345678 9;: H9":
H9":
5678=<9":
5678 [email protected]
H9ONN'@(N)<
>?83678 [email protected]
H9"[email protected]#LM
ACB0DE(678 9F
[email protected]
64G678 [email protected]
H9<<@<I
Figure 6.13: Word Order Parameter - Hierarchy 5
As an example, assume that the current status of the word order parameters
hierarchy is that shown in figure 6.12, and the status changes after reinforcing the
parameters to the one shown in figure 6.13, where subjdir is set to backward
(‘\’) and vargdir, detdir and ndir to forward (‘/’). There are several possible
grammars that are compatible with these settings, with three possibilities shown
in figures 6.2 to 6.4. However, there is a variation in terms of the compactness of
168
%++
'&&()&*
'&&()&*
"!#$!%
,.-/01 32
Figure 6.14: Word Order Parameter - Hierarchy 6
each hierarchy. In the first one (in figure 6.2), the supertype parameter gendir
has value backward, which is inherited by subjdir and ndir2, and overridden
by the 3 other parameters, where the inheritance chain is broken. In the second
hierarchy (in figure 6.3), the supertype parameter gendir has value backward,
which is inherited by subjdir, and overridden by all the other parameters, with
the inheritance chain being broken in 2 cases. In the last hierarchy (in figure
6.4), gendir is specified as forward and is inherited by all its subtypes, with
the exception of subjdir, which overrides the default value with backward,
and the inheritance chain is broken in only one place. The learner needs to find
the hierarchy that not only is compatible with the parameter settings, but that
also has the most concise encoding for the UG, and to achieve this it executes
the algorithm Compute-Probabilities-of-Supertypes. Step 1 is executed
for each of the word order supertype parameters and it divides the subtypes of
a given supertype in two groups according to the value they adopt as current
value. For instance, if we assume that v1 is forward and v2 backward, for
the supertype ndir2 both its subtypes ndir and detdir are part of the subset
prwov1 , because both are set to forward, and prwov2 is empty. The learner then
executes Step 2, because |prwov1 | > |prwov2 |, and sets the current value of the
supertype ndir2 to forward. Using the probabilities from figure 6.13, Step 2.1
sets the posterior probabilities of ndir2 to:
pndir2 (f orward) =
11
12
+
2
22
24
=
11
12
(6.21)
2
+ 24
1
=
(6.22)
pndir2 (backward) =
2
12
If the learner now executes Step 1 for the supertype gendir, which has 5
subtypes, these are divided into two groups: prwov1 = {vargdir, ndir2, ndir,
detdir}, and prwov1 = {subjdir}. In this case, the learner also proceeds to
Step 2, since |prwov1 | > |prwov2 |, and the current value of gendir is set to
forward, with its posterior probabilities computed in Step 2.1, based on the
posterior probabilities of ndir2, ndir, detdir and vargdir:
1
12
169
pgendir (f orward) =
11
12
+
11
12
+
4
22
24
+
35
36
=
67
72
(6.23)
2
1
+ 24
+ 36
5
=
(6.24)
pgendir (backward) =
4
72
The resulting parameter settings are those shown in the hierarchy in figure
6.14 which are exactly the same as those shown in figure 6.4. This is the most
concise encoding, specifying the need for exactly 2 AVSs, instead of for example,
3 in figure 6.3, or 4 in figure 6.2.
The BIPS learner has a preference for grammars (and thus hierarchies) that
not only model the triggering data well, but are also compact. Therefore, the
most probable grammar, among the ones consistent with the parameter settings,
is the one where the default inheritance hierarchy is the most concise. This is
the grammar that has the minimum number of explicitly defined AVSs, and,
consequently, makes more efficient use of the inheritance mechanism.
1
12
6.3
+
1
12
Summary
In this chapter we described the architecture of the learner. The learner has
a UG with its principles and parameters, and a learning module. Each input
sentence-logical form pair is analysed by the learner, which detects the triggers
provided and sets the parameters accordingly. The learning modules use the
BIPS algorithm during the acquisition process to set the parameters of the UG.
There are two different kinds of parameter: the categorial parameters and the
word order parameters, and they are treated in slightly different ways. Categorial
parameters control the categories that are allowed as part of the grammar and are
incrementally set. Word order parameters determine the direction of the subcategorised elements of a complex category, and they are set based on the frequency
with which their values are reinforced by the triggers. During the setting of the
parameters, the learner is searching for the grammar that is consistent with the
triggers seen so far and that is also the most concise.
170
Chapter 7
The Learning Tasks
During the learning process, there are several different aspects of language that
the learning system has to acquire. The learner starts with a UG that is very
general and only partially specified, and it has to use the input data to complete
this initial knowledge. When the learner receives a triggering input sentence,
which is a sentence annotated with a corresponding logical form and the semantic
and syntactic category assignments for each word in the sentence, it provides
several different levels of information that the learner has to process. The first
one relates to the putative categories assigned to the words by the syntax learner.
The BIPS learner needs to establish if, among the putative category assignments,
there is a valid syntactic category assignment for the sentence. Then the learner
has to establish if the categories in the VCA are part of the current grammar by
checking the corresponding categorial parameters. If not, these categories need
to be learned and the UG extended, as is described in section 7.1.
During this process, there are cases where the learner faces ambiguity between
semantic and syntactic structures, with the Categorial Principles not being able to
uniquely determine a syntactic form based only on the semantics of a word. One
such case is that of locative Prepositional Phrases that are ambiguous between
true arguments of the verb or as adjuncts, and this case is investigated in section
7.2. Once the learner establishes which is the appropriate status of the PP in
relation to the verb, the corresponding categories and the triggers expressed in
them are used for further processing.
When processing the triggers, the learner uses the information available to
determine the appropriate word order that captures this language. This learning
task is described in section 7.3.
Throughout the acquisition process the learner faces several difficulties, among
them ambiguity and noise in the input data. The problem of ambiguous triggers
is investigated in relation to PPs as arguments or adjuncts in section 7.2, and
the problem of noise is discussed in relation to the acquisition of word order in
section 7.3.
In these sections, the performance of the learner in several learning tasks is
171
discussed. We concentrate our investigations on the conditions for the learner to
converge to the target, in relation to the learning tasks defined, and how noise
and ambiguity can affect the convergence. The chapter ends with a discussion
and analysis of the performance of the learning system in the tasks investigated.
7.1
Learning Categories
The UG has 89 categorial parameters, one for each of the categories, and they
define which categories are part of the grammar. As an example, intrans-par
is a categorial parameter for the intransitive verb type shown in figure 7.1. In
the beginning of the learning process, the learner has a limited knowledge of languages, provided by the UG. The learner has a partial specification of the UG
that contains information about basic categories and about complex categories
with one complement. For these categories the corresponding categorial parameters are set as true. Initially only these categories are allowed as part of the
grammar. Then as learning progresses, the learner is faced with the task of processing more complex sentences, with the need for more complex categories. As
this happens the learner has to look for grammars that extend the UG with the
new categories. It is this task that we address in this section, where the learner
gradually acquires more complex categories.


















intrans-sign

CAT






: 






RESULT:SIGN:CAT
ACTIVE

: <!
:
 CAT-TYPE : s-cat


 M-FEATS:ALLOWED



SIGN:CAT : np
! >
DIRECTION : subjdir


: 
intrans-par
VALUE : /true
































Figure 7.1: Intransitive Verb Type Partially Expanded
The learner is looking for the grammar that adds the new categories and that
is the most compact, as discussed in section 6.2. The most compact grammar
is the one where the minimum number of AVSs needs to be explicitly specified.
To find this grammar, one assumption that is made is that the learner uses the
algorithm defined by Light [1993], which finds an optimal insertion place for a
new type in the hierarchy. This is the insertion place where the minimum number
of parent types provides the maximum number of attributes required by the new
type. In terms of verbs, the learner starts with knowledge about the basic verbal
category for intransitive verbs and it has to dynamically expand the hierarchy in
order to add the appropriate types corresponding to more complex subcategorisation frames. The learner is guided in this search by the Categorial Principles
that find an appropriate syntactic structure for a given semantic predicate. As
172
an example, suppose the learner receives a sentence like:
• (7.1) You have one
paired with the meaning:
{have(
1
,
2
,
3
), you(
4
,
2
), one(
5
,
3
)},
where the predicate of each word is determined to be:
{have1 =have(a,b,c), you1 = you(d,e), one1 = one(f,g)}
and they are paired with the following set of putative category assignments:
{(you = NP, have = (S\NP/NP), one = NP)}
According to the Categorial Principles, the categories assigned for these semantic
predicates are correct. S\NP/NP is the category for transitive verbs, shown
in figure 7.2, and this category provides triggers for the parameter trans-par
that allows transitive categories as part of the grammar, and for the parameters
subjdir and vargdir, encoding, respectively, the direction for the subject and
for the object of the verb.






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












trans-sign

CAT







: 








CAT-TYPE : s-cat
M-FEATS:ALLOWED



ACTIVE : <! SIGN:CAT : np
DIRECTION : subjdir,


 SIGN:CAT : np
! >
DIRECTION : vargdir
RESULT:SIGN:CAT
: 

:
trans-par




















Figure 7.2: Transitive Verb Type Partially Expanded
If transitive verbs are already part of the grammar, the parameter trans-par
associated with transitive verbs is set as true, and the triggers are used to set
the word order parameters, subjdir and vargdir, as explained in section 6.2.1.
On the other hand, if trans-par is set as false, then transitive verbs are not part
of the hierarchy yet. For instance, assuming that the current grammar is the one
shown in figure 7.3, possible hierarchies showing different insertion places for
the transitive verb type are shown in figures 6.5 to 6.7, repeated here as 7.4
to 7.6. In these figures the information that needs to be explicitly specified is
displayed in bold font. Since the hierarchy needs to be gradually expanded to
account for more complex cases, the learner uses inheritance to take advantage of
173
Figure 7.3: Current Hierarchy
! Figure 7.4: Insertion Place for the Transitive Verb Type - 1
the information already acquired, in order to obtain the most concise grammar. 1
Because the learner is looking for a compact hierarchy, the current hierarchy
needs to be expanded so that the minimum number of specifications needs to
be added to it, making maximum use of the information already contained in it.
The learner finds that the intransitive verb type with category S|NP, shown in
figure 7.1, is an optimal supertype for a transitive verb type, as shown in the
hierarchy in figure 7.4, because only the information shown in figure 7.7 would
need to be added, and it verifies that intrans-par, its corresponding categorial
parameter, is set as true. As a consequence, the learner adds trans-par as a
subtype of intrans-par, setting it to true, and adds the transitive verb type as
a subtype of the intransitive verb type.
The other options shown in figures 7.5 and 7.6 correspond to the TDFSs
1
In this work, the assumption is made that the definitions of the categories and categorial
parameters are all available as part of the UG. Then, as the learning process takes place, these
definitions are added as part of the hierarchy in optimal places so that the resulting hierarchy is
the most concise. However, this assumption does not alter the results obtained by the learning
system.
174
Figure 7.5: Insertion Place for the Transitive Verb Type - 2
Figure 7.6: Insertion Place for the Transitive Verb Type - 3









trans-sign



: trans-par  
 RESULT:SIGN:CAT:M-FEATS:ALLOWED






CAT :  ACTIVE : <!
SIGN:CAT
: np



/!
>
,


> DIRECTION : vargdir

Figure 7.7: Specification of Transitive Verb Type
shown in figures 7.8 and 7.9, respectively. These options require more information to be encoded in the new type.
With the addition of this category to the hierarchy, the learner becomes able
to successfully process sentences containing transitive verbs. After that, when
a ditransitive verb is presented to the learner, it needs to extend the hierarchy
by adding the appropriate type for the category S|NP|NP|NP. The most concise
grammar requires the ditransitive verb type to be inserted as a subtype of the
transitive verb type that encodes the category S|NP|NP. Also, ditrans-par, the
categorial parameter associated with ditransitive verbs, has to be added as a
subtype of trans-par. This means that a ditransitive verb can only be learned
after the category for transitive verbs is learned and added to the hierarchy. Thus,
if trans-par is set as true, then ditrans-par can also be set as true, as is the
case in this example. Otherwise, if trans-par is false, the ditransitive verb type
175
















trans-sign

RESULT:SIGN:CAT:M-FEATS:ALLOWED





 ACTIVE : <! SIGN:CAT : np


DIRECTION : subjdir,
CAT : 





 SIGN:CAT : np
! >

DIRECTION : vargdir
trans-par
:
















Figure 7.8: Transitive Verb Type - Alternative 1




















trans-sign

CAT







: 








RESULT:SIGN:CAT :  CAT-TYPE : s-cat
M-FEATS:ALLOWED



ACTIVE : <! SIGN:CAT : np
DIRECTION : subjdir,


! >
 SIGN:CAT : np
DIRECTION : vargdir

:
trans-par




















Figure 7.9: Transitive Verb Type - Alternative 2
cannot yet be added as part of the grammar, and the learner ignores the sentence.
As a consequence of the requirement for the most concise encoding, an implicit
ordering on the learning of categories is obtained, with categories being learned
in incremental order of complexity using the maximum amount of information
already acquired by the learner. For example, an intransitive verb subcategorising
for one complement is less complex than a transitive verb subcategorising for two
complements which is less complex than a ditransitive verb subcategorising for
three complements.


































CAT:ACTIVE








: <!
SIGN
:

: 
: 
np-subj-sign
SEM:INDEX :
np-obj-sign
SEM:INDEX

:
np-obl-sign
SEM:INDEX :


 RELN : reln 


 SIT : index 


! >
<!

 ARG1 : 1



 ARG2 : 2


ARG3 : 3
SIGN
SEM:RESTR
SIGN

: 
2
3
1





! >





































Figure 7.10: Possible Linking Pattern - 1
As the learner extends its grammar with more complex categories, these categories also introduce more complex linking patterns between the semantic argu176


































CAT:ACTIVE





: <!
SIGN

SIGN

: 
:

 np-subj-sign
SEM:INDEX :
np-obj-sign
SEM:INDEX
:

SIGN :  np-obl-sign
SEM:INDEX :


 RELN : reln 


 SIT : index 

! >
SEM:RESTR : <! ARG1 : 2




 ARG2 : 3


ARG3 : 1


2
3
1













! >

































Figure 7.11: Possible Linking Pattern - 2


































CAT:ACTIVE






: <!
SIGN
SIGN

: 

: 
np-subj-sign
SEM:INDEX :
np-obj-sign
SEM:INDEX

:
np-obl-sign
SIGN
SEM:INDEX :


 RELN : reln 


 SIT : index 

! >
SEM:RESTR : <! ARG1 : 3




 ARG2 : 1


ARG3 : 2


: 
2
3
1





! >

































Figure 7.12: Possible Linking Pattern - 3
ments and the syntactic complements.2 Therefore, when the grammar is incrementally constructed, the linking constraints are also incrementally added to it.
When learning new and more complex linking patterns, the learner may be uncertain as to which of the possible linking options, given the semantic arguments
and syntactic complements, it should choose. For example, when an oblique
transitive verb is learned, there are six different linking possibilities among the
syntactic complements and semantic arguments, as shown in figures 7.10 to 7.15.
The learner needs to decide which of these six options it is going to adopt, but
without any criterion one option is as good as the other. One source of bias
for the learner in this decision is the requirement for the most concise grammar,
following the MDL-style bias. Thus, the learner examines the linking patterns
it already has, and uses this information to decide among these options. Let
us assume that the learner has already decided that a transitive verb type is an
optimal supertype and has also determined its corresponding linking pattern as
that shown in figure 7.16. Then, the learner determines that the most concise
2
Possible linking patterns in English are described in section 4.2.4.
177


































CAT:ACTIVE





: <!
SIGN

SIGN

: 
:

 np-subj-sign
SEM:INDEX :
np-obj-sign
SEM:INDEX
:

SIGN :  np-obl-sign
SEM:INDEX :


 RELN : reln 


 SIT : index 

! >
SEM:RESTR : <! ARG1 : 1




 ARG2 : 3


ARG3 : 2


2
3
1













! >

































Figure 7.13: Possible Linking Pattern - 4


































CAT:ACTIVE






: <!
SIGN
SIGN

: 

: 
np-subj-sign
SEM:INDEX :
np-obj-sign
SEM:INDEX

:
np-obl-sign
SIGN
SEM:INDEX :


 RELN : reln 


 SIT : index 

! >
SEM:RESTR : <! ARG1 : 3




 ARG2 : 2


ARG3 : 1


: 
2
3
1





! >

































Figure 7.14: Possible Linking Pattern - 5
encoding is obtained by choosing the option in figure 7.10 which only requires
a minimum of additional information to be encoded in the grammar3 , as shown
in figure 7.17. All the other possibilities would require the addition of more
information than that, and they are less interesting for the learner. The use of
a default inheritance hierarchy allows the linking information to be passed from
supertype to subtype. This means that a subtype will get most of its linking
constraints for free from its supertype. It will only need to specify the linking
for the remaining arguments, and there are only a finite number of possibilities
for this linking. Moreover, from these possibilities, all the patterns that are incompatible with the inherited information are ruled out. In this way, the default
inheritance hierarchy not only reduces the amount of linking information that
needs to be learned, but also rules out possible patterns that are incompatible
with the inherited information. Consequently, the learner makes very efficient use
3
Also, as discussed in section 4.2.4, the same linking pattern is adopted by ditransitive
verbs with the rule of permutation rotating the elements in the subcategorisation list, until an
appropriate ordering is obtained.
178


































CAT:ACTIVE





: <!
SIGN

SIGN

: 
:

 np-subj-sign
SEM:INDEX :
np-obj-sign
SEM:INDEX
:

SIGN :  np-obl-sign
SEM:INDEX :


 RELN : reln 


 SIT : index 

! >
SEM:RESTR : <! ARG1 : 2




 ARG2 : 1


ARG3 : 3


2
3
1













! >

































Figure 7.15: Possible Linking Pattern - 6
























CAT:ACTIVE



: <!
SIGN


: 
np-subj-sign
SEM:INDEX :
np-obj-sign
SIGN
SEM:INDEX :


RELN : reln 



SEM:RESTR : <! SIT : index ! >

 ARG1 : 1
ARG2 : 2


: 
2


! >
1























Figure 7.16: Specification of Transitive Linking Pattern Expanded
of the default inheritance hierarchy to learn and encode new linking information.
There are cases where there is a mismatch between the semantic structure,
the subcategorisation frame, and the linking constraint. One interesting case is
that of raising verbs, which we consider to be in the canonical form in a sentence
like It seems that John runs, where seems is an intransitive raising verb. For
such a verb, there is a mismatch between the semantic argument structure and
the syntactic subcategorisation frame. It has only one semantic argument, a
propositional argument, and it is syntactically realised as an S. However, this
cannot be the only subcategorised category of the verb, as the ungrammaticality
of the sentence *Seems that John runs indicates. As required by the Categorial
Principles every sentence must have a subject, which means that every verb must
subcategorise for a subject. Consequently the subcategorisation frame for such a
verb is S/S\NP. Thus, an intransitive raising verb is a one-place predicate, but
subcategorises for two complements: an NP and a predicative complement. As
such a construction did not occur frequently enough in the processed sentences to
be learned, we did not implement a solution for dealing with them, but in what
follows we present the outline of a possible treatment.
When the learner is faced with such a raising verb containing only one semantic argument and two syntactic complements, there is an indeterminacy between
179











ORTH
:
orth
CAT:ACTIVE
SEM:RESTR
: <!
: <!
>
,
>
ARG3
:


,
3
SIGN
!>

: 
np-obl-sign
SEM:INDEX
:
3


! >











Figure 7.17: Specification of Oblique Transitive Linking Pattern
two possible linking constraints:
• the semantic argument is linked to NP, which is the pattern adopted by
most verbs, or
• the semantic argument is linked to S.
As the canonical form has the NP subject occurring as a pleonastic or expletive subject, this form indicates the absence of a corresponding semantic role
[Hyams 1986], and rejects the first hypothesis. Thus the canonical form of the
raising construction with a pleonastic or expletive subject gives evidence for the
learner to select the second linking pattern, where the semantic argument is linked
to S. Related raising constructions such as that in the sentence John seems to
run can be obtained by applying a lexical rule to the intransitive raising verb,
which generates the derived category S/(S\NP)\NP from S/S\NP. In this way,
as the categories are incrementally learned, so are the linking patterns.
7.2
Learning from Ambiguous Triggers
The learner uses the Categorial Principles to determine appropriate syntactic categories for the semantic predicates used as input. In most cases, the Categorial
Principles guides the learner to find the required syntactic categories. However,
there are cases where it is not possible to uniquely determine an appropriate
subcategorisation frame for a given semantic predicate. In this section, we discuss one case where the learner faces ambiguity when choosing an appropriate
subcategorisation frame for the semantic structure associated with a particular
word: locative Prepositional Phrases (PPs) occurring with verbal constructions
as subcategorised complements or non-subcategorised adjuncts. The ambiguity
between these cases arises because using this particular logical form representation, in the case of locative PPs, the logical form describing the verb with an
argument PP is similar to that describing the verb with an adjunct PP.4 For
example, the sentence:
4
It may be the case that using another representation for the logical form this ambiguity
does not arise.
180
• (7.2) Bill swims across the river
with logical form:
{swim(
1
,
2
), bill(
3
,
2
), across(
1
,
4
), the(
5
,
4
), river(
,
6
4
)}
shows a case where the PP is an argument of the verb swim, and where the appropriate subcategorisation frame for the verb should include the PP: (S/PP)\NP,
as a locative intransitive sign. On the other hand, the sentence:
• (7.3) The dog chases the cat in the garden.
with logical form:
{chase( 1 , 2 , 3 ), the( 4 ,
the( 9 , 8 ), garden( 10 , 8 )}
2
), dog(
5
,
2
), the(
6
,
3
), cat(
7
,
3
), in(
1
,
8
),
exemplifies a case where the PP is an adjunct. Thus it should not be included in
the subcategorisation frame of the transitive verb chase, which is (S/NP)\NP. For
both sentences, the logical form has a similar structure, with both a verbal and
a locative predicate, and so the logical form cannot be used to help the learner
resolve the ambiguity: given the logical forms {swim( 1 , 2 ) across( 1 , 5 )} and
{chase( 1 , 2 , 3 ) in( 1 , 8 )}, which syntactic category should the learner choose
for each of these verbs? This ambiguity constitutes a significant problem for
the learner, since it has to decide whether or not a given PP is functioning as
a complement of a verb and should be included as part of the subcategorisation
frame of the verb, or if it is working as an adjunct and should not be included
as a subcategorised complement of the verb. Three different cases to which the
learner is exposed are identified, based on Pustejovsky [1991 and 1995], Wechsler
[1995] and Verspoor [1997], with the PP occurring as an obligatory argument, as
an optional argument, or as an adjunct5 :
1. The PP is an obligatory argument of the verb. For certain verbs
the PP is an obligatory argument of the verb and should be included in
its subcategorisation frame. An instance of this case is the verb put, in
sentence 7.4:
• (7.4) Mary put the book on the shelf,
with logical form:
{put( 1 , 2 , 3 ), mary(
the( 8 , 7 ), shelf( 9 , 7 )}.
4
,
2
), the(
5
,
3
), book(
6
,
3
), on(
1
,
7
),
5
In this work we classify PPs in terms of these three cases, even though more fine-grained
classifications can be used as in [Pustejovsky 1995].
181
In this sentence put occurs with a locative PP. Also, as the ungrammaticality of sentence 7.5 suggests, this verb requires a locative PP:
• (7.5) * Mary put the book
The appropriate syntactic category for the verb6 is ((S/PP)/NP)\NP.
2. The PP is an optional semantic argument of the verb. For example,
a verb such as float can occur with a locative PP, as in sentence 7.6, from
Pustejovsky [1995, p. 126]. In 7.6 the motion verb float is modified by a
directional PP which is an optional argument of the verb:
• (7.6) The bottle floated into the cave.
with logical form:
{float(
,
1
), the(
2
3
,
), bottle(
2
4
,
2
), into(
1
,
5
), the(
6
,
5
), cave(
7
,
5
)}.
This verb may also occur without the PP, as in sentence 7.7:
• (7.7) The bottle floated.
with logical form:
{float(
,
1
), the(
2
3
,
), bottle(
2
4
,
2
)}
This is a case of a verb that can occur in both constructions with the PP
being a semantic argument, which, when occurring, must be included in
the subcategorisation frame of the verb. Consequently, the appropriate
category for the verb float in the first sentence is (S/PP)\NP, and in the
second is S\NP.
3. The PP is an adjunct. Adjuncts modify the logical form of the sentence, but are not part of the subcategorisation frame of the verb. The
PP in the park in sentence 7.8 is an example of an adjunct that is neither
part of the semantic argument structure of the verb kiss nor part of its
subcategorisation frame:
• (7.8) Bill kisses Mary in the park,
whose logical form is:
{kiss(
1
,
2
,
3
), bill(
4
,
2
), mary(
5
,
3
), in(
1
,
6
), the(
7
,
6
), park(
8
,
6
)}.
This verb can also occur without the PP, as in sentence 7.9:
• (7.9) Bill kisses Mary,
whose logical form is:
{kiss(
1
,
2
,
3
), bill(
4
,
2
), mary(
5
,
3
)}.
The appropriate syntactic category for the verb in both sentences is S/NP\NP.
6
This work does not include, in its investigation, elliptical or noisy constructions. Therefore,
the sentences analysed and the frequencies reported exclude these cases.
182
When faced with a locative PP, the learner has to identify which of these cases
is appropriate. The required subcategorisation frame is determined independently
for each verb sense. It depends on the semantic type of the verb, and on its
frequency of occurrence with a particular subcategorisation frame and predicate
argument-structure combination.
In order to determine if a locative PP is an obligatory argument of the verb,
the learner uses frequency information about the occurrence of each verb with
locative PPs. If the frequency with which they occur together is above a certain
threshold, the PP is considered to be an obligatory argument of the verb. In
an analysis of all the mother’s sentences in the entire Sachs corpus, only two
occurrences of put without the locative PP were found: one seems to be an instance of an elliptical construction, and the other a derived sense. The frequency
with which put occurs with a locative PP indicates that the PP is an argument
of the verb, and it needs to be included in the subcategorisation frame of the
verb. On the other hand, for verbs like float and kiss in sentences like 7.6 to 7.9,
the locative PP is an occasional constituent, with the semantics of the sentence
including the location predicate only in these cases. The occasional occurrence
of PPs indicates that they are not obligatory PP arguments.
Thus, if the learner detects the occurrence of the verbal predicate above a
certain threshold with the locative predicate, then it considers that the latter is
required as an argument in the subcategorisation frame of the verb. In this case,
the threshold is set to 80% of the total occurrences of a verb. This is high enough
for discarding adjuncts and optional arguments that occur occasionally, and at
the same time is not high enough to be affected by the occurrence of noise. We
also experimented with other values, but this had optimal effect.
If the frequency is not above the threshold, then the PP can be either an
optional argument or an adjunct. To determine if a PP is an optional argument,
the learner checks if the preposition can be semantically selected by the verb. This
approach to identify non-obligatory argument PPs follows Wechsler’s proposal of
semantically motivated preposition selection [Wechsler 1994 and 1995], where
a PP is an argument of a verb if it can be selected by the verb on pragmatic
grounds. Pragmatic knowledge is represented in terms of a hierarchy of types
and it is used to classify verbs and prepositions. A fragment of such a hierarchy
is shown in figure 7.18. Following Wechsler’s approach a verb such as talk, which
is of type communicative-act, can select as its argument a preposition such
as to, which is of type comm-to, because these two types unify on the world
knowledge hierarchy, as in Bill talks to Mary. On the other hand, this verb does
not select a preposition such as across of type directed-motion as its argument,
because their types do not unify. However, this preposition can be selected as the
argument of the verb swim in sentence 7.2, which is a motion-act type. In this
way, the pragmatic knowledge confirms certain PPs (e.g. across) as arguments
of some verbs (e.g. swim), while rejecting others.
If a locative PP is rejected as argument of a verb on pragmatic grounds, then
183
%&' )( %*' ,+ $.-,/,0
! "#
$.-,/
$$
Figure 7.18: Fragment of Hierarchy of World Knowledge
the PP is treated as an adjunct and is not included in the subcategorisation frame
of the verb. Once the learner decides which is the case for a particular verb
PP combination, it uses the triggering information, including the appropriate
subcategorisation frame of the verb, for further processing.
7.2.1
Argument or Adjunct?
This section discusses how the proposed approach helps the learner facing ambiguous triggers in relation to locative PPs as arguments or adjuncts. For this
task, the learner is evaluated in terms of three different verbs: put where the PP
is an obligatory argument, come, where the locative PP is an optional argument,
and draw (in the sense of drawing a picture) where the PP is an adjunct. These
verbs are representative of each case and the sentences in which they occur are
taken from the mother’s section of the complete Sachs corpus, which is the largest
of the parents’ sections. The status of the locative PPs occurring with these verbs
is determined following syntactic tests for argument structure7 . The specific test
used for determining the status of the PP is the “do so” test, which is a standard
test for argument structure. In this test, the claim is that a complete complement
can be replaced by “do so”. In the case of obligatory arguments, only the full
constituent verb PP or verb NP PP can be replaced by do so, while in the
case of adjuncts, the verb or verb NP constituent can also be replaced by do
so. The sentences 7.9 to 7.17 indicate that the PPs are arguments of the verbs
put and come, and adjuncts of the verb draw.
• (7.9) You put Goldie through the chimney
7
For a discussion about several tests for determining argument structure see Verspoor [1997].
184
• (7.10) You put Goldie through the chimney and Bob also did so
• (7.11) * You put Goldie through the chimney and Bob did so through the window
• (7.12) You came from the garden
• (7.13) You came from the garden and John also did so
• (7.14) * You came from the garden and John did so from the kitchen
• (7.15) You drew in the park
• (7.16) You drew in the park and John also did so
• (7.17) You drew in the park and John did so in the garden
In the mother’s sentences from the entire Sachs corpus, the occurrence of these
verbs with locative PPs is as shown in table 7.1. This table shows in the first
column the verb, in the second the frequency of occurrence of the particular verb
sense with a locative PP, in the third the frequency of occurrence of the verb sense
without a locative PP, and in the fourth the total occurrences. Only sentences
which contain the verbs in the relevant sense are considered, and sentences where
the verb occurs with the locative PP and with particles are not considered.
Table 7.1: Frequency Information about Locative PPs
Verb
Frequency Frequency
Total
with PP
without PP
put
137
2
139
come 24
8
32
draw 9
12
21
The first verb, put, is a verb that occurs mostly with locative PPs, as reflected
by the frequency in table 7.1, and where the locative PPs are considered to be
true arguments of the verb, following the “do-so” test. The sentences that occur
without the locative PP (table 7.2) correspond to 1.4% of the total.
Table 7.2: Sentences with put without a Locative PP
Sentence
What are you putting in braids
We put chocolate
The first sentence has a derived sense of put, where the PP is not locative,
in spite of the subcategorisation frame being similar (((S/PP)/NP)\NP). The
second of these sentences seems to be elliptical and needs a context in order to
185
be completely acceptable (from the Sachs Corpus).
• (7.18) No, we don’t put glasses in the milk.
• (7.19) We put chocolate.
The verb come occurs in the corpus with both constructions, as exemplified
in sentences 7.12 to 7.14 and 7.20, with the locative PP occurring in 75% of
the sentences. Consequently, frequency information disconfirms come as having
obligatory PP arguments. In the case of come the PP is an optional argument,
and sentences without it are also acceptable, as sentence 7.20 shows. Nonetheless, the locative PP is an argument of the verb come [Levin 1993], as can be
confirmed by the “do so” test (sentences 7.12 to 7.14).
• (7.20) I’ll come
As the frequencies in table 7.1 indicate, draw is a verb that can frequently
occur in each of these constructions, as exemplified in sentence 7.15 to 7.17 and
7.21. From the 22 sentences in the corpus containing draw, 57% occur without
the locative PP, and when the locative PP occurs, it is considered to be an adjunct according to the syntactic test for argument structure.
• (7.21) I am not drawing
Upon receiving an input sentence, the learner attempts to disambiguate the
PP as argument or adjunct of the verb by first checking if the frequency of
occurrence of the verb with locative PPs is above the threshold of 80%, in which
case the PP is considered to be an obligatory argument of the verb. Otherwise,
the learner checks if the verb can select the PP on pragmatic grounds. If so, the
PP is an optional complement of the verb. On the other hand, if this is not the
case, then the PP is considered to be an adjunct. Once the learner determines
which is the appropriate case and selects a suitable subcategorisation frame, then
this information is used to set the parameters of the UG.
The learner is given as input sentences annotated with logical forms, and
semantic and syntactic categories for the words in each sentence. In the input
sentences, each of these verbs occurs with the patterns and frequencies presented
in table 7.1. The results obtained for each of these three verbs are shown in
table 7.3. In this table the first column shows the verb, the second the number
of sentences used as input for each of the subcategorisation frames, and in the
third, the number of times the learner correctly disambiguates the locative PP
for each of the subcategorisation frames.
The learner correctly selects the appropriate subcategorisation frame in all of
the cases, which confirms the effectiveness of the proposed approach to disambiguate locative PPs.
186
This experiment used three verbs representing each of the cases that the
learner has to face when a locative PP is encountered in the input data:
• obligatory arguments, disambiguated with frequency information,
• optional arguments, selected on pragmatic grounds, and
• adjuncts.
In terms of frequency of occurrence of the verbs with the locative PPs, other
verbs in the mother’s sentences from the entire Sachs corpus also have a similar
pattern, with the locative PP being frequent for arguments of the verb, and less
frequent than the non-locative construction for the case of adjuncts:
• stay, which according to the “do-so” test has an obligatory locative PP
argument, occurs in 12 sentences in the corpus (such as sentence 7.22), and
in all of them the locative PP is present,
• eat, which according to the test does not have a locative PP argument,
occurs in 81 sentences as a transitive verb (such as sentence 7.23), and in
only 1 of these it has a locative PP, and
• play, which also does not have a PP argument, is in 10 sentences in the
corpus, as an intransitive verb (as in sentence 7.24), and in 4 of those it has
a locative PP.
These results indicate that it is indeed possible for the learner to disambiguate
between locative PPs as arguments or adjunct based on semantic compatibility
and frequency information.
• (7.22) That’s because the piggy had to stay at home.
• (7.23) We can’t eat it now.
• (7.24) I think she just wants to go out to play.
Table 7.3: Disambiguation of Locative PPs
Verb
Input
Sentence
put
locative PP = 137
non-locative PP = 2
come locative PP = 24
non-locative PP = 8
draw locative PP = 9
non-locative PP = 12
187
Correctly
Disambiguated
137
2
24
8
9
12
7.3
Learning Word Order Parameters
Word order parameters reflect the underlying order in which constituents occur
in different languages. There are 18 word order parameters defined, based on
typological considerations ([Croft 1992] and [Comrie 1981]), and they are embedded in an inheritance hierarchy, as explained in section 4.5. As defined, the
UG allows for languages with the four basic word orders, defined in terms of the
canonical order of the verb (V), subject (S) and object (O): SVO, SOV, VSO
and OVS. These major word order groups are obtained by setting the parameter
subjdir, for the direction of the subject, and vargdir, for the direction of the
other verbal arguments:
• SVO: subjdir = backward and vargdir = forward,
• SOV: subjdir = backward and vargdir = backward,
• OVS: subjdir = forward and vargdir = backward and
• VSO: subjdir = forward and vargdir = forward8 .
Specific languages inside each of these major language groups are allowed by
the other word order parameters, such as ppdir that defines if the language
accepts prepositions or postpositions, and reldir that defines if relative clauses
are allowed before or after the noun they modify [Comrie 1981]. In the beginning
of the learning process, the partial specification of the UG needs to be set for
direction according to the input data. As the learner starts receiving input data, it
tries to analyse the data, and in order to get successful derivations consistent with
the logical form, the learner has to set the direction of the relevant parameters
for the target language. If the learner is exposed to English, which is an SVO
language, the learner has to set, among other parameters, the subjdir parameter
to backward, as the NP subjects occur to the left of the verb, and the vargdir
parameter to forward, because other verbal complements occur to the right of
the verb. The setting of these parameters is also executed in such a way as to get
the most concise encoding for the grammar, taking into account the information
flow in the inheritance hierarchy. In order to do so, the learner collects frequencies
for word order parameters, reflecting the occurrence of each of the possible values
of a parameter in the triggering data. It uses these frequencies to decide which
of the values should be used to set the parameter, as described in section 6.2.1.
These frequencies also help the learner deal with noisy and ambiguous triggers
that can be present in the input data.
8
Other possible word orders such as VOS and OSV can be obtained by adding another
parameter to the current model of the UG that inverts the order of the subject and objects of
the verb with respect to the semantic arguments, as done by Briscoe [1997-2000]. However, the
orders obtained by the current UG are varied enough for the proposed investigation.
188
In this work we investigate the performance of the learner in setting the word
order parameters, in a number of experiments where different environments are
defined, with different degrees of noise and with different starting points. In each
learning cycle, the learning system receives sentences from the annotated Sachs
corpus paired with logical forms as input. This English corpus has an underlying
SVO order and a predominantly right branching structure. The sentences in the
input corpus are presented to the learner only once, sequentially, in the original
order.
After a sentence is assigned semantic and syntactic categories, if a VCA is
among the category assignments, then the sentence is processed, with the triggers
expressed in the sentence being detected and used to set the parameters of the
UG. As the sentences are processed, the learner sets the parameters to reflect the
constructions found in these sentences, and the order in which the constituents
occurred, using the algorithms described in chapter 6.
This learning task is investigated under several different conditions. These
conditions provide different environments for the learner during the acquisition
process. They can vary with respect to the starting point for the learning process,
and with respect to the amount of noise and ambiguous triggers present in the
input data. As the assignments made by the syntax learner for a given sentence
may vary slightly at each learning cycle, each condition is run 10 times and the
results are reported in relation to the averages obtained. In these experiments,
the learner is initialised with all word order parameters unset, unless otherwise
stated. In relation to the categories in the grammar, all the categorial parameters
are false, except those for the basic categories and for the complex categories with
one subcategorised complement, unless otherwise stated.
7.3.1
The Unset Learner: a Basic Case
The unset learner is initialised with all word order parameters being unset. It has
the convergence displayed in table 7.4 and in figure 7.19, with an average of 129.1
triggers that have VCAs and that can be used to set the parameters, out of 1,517
sentences. With these triggers, 8.1 parameters in average are set out of a total of
18 parameters, resulting in 13.5 parameters being correct according to the target
because of the inheritance of default values from the supertype parameters.
Table 7.4: Convergence of the Unset Learner
Learner Triggers
Unset
129.1
Parameters
Correct
13.5
Parameters
Set
8.1
As the output of the syntax learner may vary slightly at each run, the learner
189
may be given a somewhat different group of sentences for setting the parameters
at each run. In this way, some sentences that are used to set parameters in one
run may not be available in the next one. As a consequence, the parameters that
are set in one run may not be set in the next, since the learner may not have
triggers for doing that. However, this variation is small, and throughout each of
the 10 runs, the same parameters tend to get set.
,
+ *( )*
' & '(
-./10
!"$#%
Figure 7.19: Performance of the Unset Learner
Figure 7.20 shows the convergence pattern obtained in a typical learning cycle
for the unset learner, for the subjdir, vargdir, ppdir and gendir parameters.
This figure shows how the subjdir parameter is set early on in the learning
process, and how the value of gendir is strongly influenced by this, so that
gendir is set as backward until there are more parameters set as forward than
backward, around trigger 16.
In the input data there are triggers for an average of 8 parameters, and all
of them are correctly set in relation to the target. However, because of the
inheritance mechanism, even though only 8 parameters are set this resulted in
13.5 of the 18 parameters having the correct value according to the target, since
they inherit by default the value of their supertypes. Thus, the encoding of
190
7: >
:=;
;<
4 59
: 95
7 896
45
#)
#(
#'
&
#%
$
#"
!
[email protected] * EGFH* !
$
&
(
,-/. 001*-32
*
+!
Figure 7.20: Convergence of the Unset Learner
parameters in terms of a default inheritance hierarchy speeds up the convergence
to the target. As a consequence, the learner is successfully converging in the
direction of the target even with a limited amount of input data.
7.3.2
Different Starting Points
The UG is defined with its parameters that are set according to the data, but how
should the parameters be initialised in the beginning of the learning process? In
the previous experiment, the learner is initialised with all word order parameters
unset, and it succeeds in setting its parameters, given the amount of triggering
data available. However, Chomsky [1981] suggests that some of the parameters
may have an initial default value, which is retained in the absence of incompatible
input during the learning process. Moreover, Hyams [1986] and Lightfoot [1991],
among others, also propose the use of default values as a way of preventing
the learner from converging to a superset grammar. Should the learner start
with unset parameters, or should it have a bias towards a group of languages?
How do the different initialisations affect the convergence of the learner? In
191
this section one set of experiments is described, where five different learners are
defined, corresponding to five different initialisations of the parameter settings of
the UG. In these experiments we investigate how the initialisations - or starting
points - of the learners influence convergence to the target grammar. The first
one, the unset learner, is initialised with all parameters unset, as in the previous
section. It is the basic case against which the others can be compared. The
other learners, the default learners, are each initialised with default parameter
values corresponding to one of four basic word orders, defined in terms of the
canonical order of the verb, subject and objects: SVO, SOV, VSO and OVS. The
parameters subjdir, vargdir and gendir of the default learners are set according
to each of the basic orders, with gendir having the same direction as vargdir,
and all the other parameters having unset values. These parameters have the
prior and posterior probabilities of 0.1 for one value and 0.9 for the other, as
shown in table 7.5. In these tests, two sets of weights corresponding to the prior
and posterior probabilities of the parameters are used, as shown in table 7.6. The
learners in Learners-10 are initialised with lighter weights (1/10 and 9/10) than
those in Learners-50 (5/50 and 45/50), which are initialised with much heavier
weights. The latter are used to investigate the effect of such a heavy initialisation
in the performances of the learners. In this case, even though the probabilities
are the same as in Learners-10, the weights are much stronger and that causes an
impact on the number of triggers needed by the learner to converge to the target
value. This set of experiments investigates how the different learners perform in
a normal environment with a limited English SVO corpus as input. The results
obtained in each of these conditions are now described.
Table 7.5: Initialisations of the Different Learners
Learners Direction
SVO
backward
forward
SOV
backward
forward
OVS
backward
forward
VSO
backward
forward
Subjdir Vargdir Gendir
0.9
0.1
0.1
0.1
0.9
0.9
0.9
0.9
0.9
0.1
0.1
0.1
0.1
0.9
0.9
0.9
0.1
0.1
0.1
0.1
0.1
0.9
0.9
0.9
Condition 1: Learners-10
In the first condition, the parameters subjdir, vargdir and gendir of the default
learners are initialised as shown in table 7.7. The results from the first experiment
192
Table 7.6: Initial Weights of the Different Learners
Learners
Weights
Learners-10 0.1 = 1/10
0.9 = 9/10
Learners-50 0.1 = 5/50
0.9 = 45/50
(table 7.8) show no significant variation in the performances of the different
learners. This is the case with the number of parameters that are correct in
relation to the target, with an average of 13.5 parameters out of 18, and also
with the number of parameters that are set given the triggers available, with an
average of 8.1 parameters out of 18, as shown in figure 7.21.
Table 7.7: Initialisations of the Different Learners-10
Learners Direction Subjdir
SVO
backward 0.9 =9/10
forward
0.1 =1/10
SOV
backward 0.9 =9/10
forward
0.1 =1/10
OVS
backward 0.1 =1/10
forward
0.9 =9/10
VSO
backward 0.1 =1/10
forward
0.9 =9/10
Vargdir
Gendir
0.1 =1/10 0.1 =1/10
0.9 =9/10 0.9 =9/10
0.9 =9/10 0.9 =9/10
0.1 =1/10 0.1=1/10
0.9 =9/10 0.9 =9/10
0.1 =1/10 0.1 =1/10
0.1 =1/10 0.1 =1/10
0.9 =9/10 0.9 =9/10
Table 7.8: Convergence of the Different Learners - Condition 1
Learners Triggers
Unset
SVO
SOV
OVS
VSO
129.1
129.1
133
132
132
Parameters
Correct
13.5
13.5
13.6
13.5
13.5
Parameters
Set
8.1
8.1
8.3
8
8
The only difference between them is the time needed for each learner to con193
verge: the closer the starting point of the learner is to the target, the faster it
converges, as shown in figure 7.22 for the subjdir parameter. This figure shows
all the learners converging to the target value, with high probability, and with a
convergence pattern very similar to the one presented by the unset learner. Even
those default learners that are initialised with values incompatible with the target soon overcome this initial bias and converge to the target. A similar pattern
occurs for vargdir and gendir.
48
76
56
9;:1<
43
23
=?>[email protected]@ :*B<
!#"%$'&
"(*),+-
".),(/+0
),(#"1+-
(*"/),+-
Figure 7.21: Learners-10 in a Normal Environment
Condition 2: Learners-50
The results in the previous condition did not show any significant difference
between the performances of the different learners. The next experiment tests
how the use of stronger weights to initialise the learners affects their performances,
given the limited amount of input data. The parameters subjdir, vargdir and
gendir are initialised with stronger weights (table 7.9). These weights provide
an extreme bias for each of the learners. In this condition, the learners are tested
again in a normal noisy environment.
The results (table 7.10) show that the learners once more have similar performances regardless of the initialisations. An average of 13.5 correct word order
parameters is obtained, with 9 out of 18 parameters being set. Figure 7.23 shows
the convergence patterns presented by these learners for the subjdir parameter.
Once again, the learners that are initialised with values compatible with the target have a faster convergence pattern, as can be seen for the SOV and SVO
learners. Nevertheless, the overall speed of convergence is much slower than in
the previous condition.
194
*
BE I
EHF
FG
? @D
E [email protected]
B CD
? @A
')(-3
')(-2
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')(-/
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')(*
'
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*
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+*
!"%$
!&$
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$
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6798 :5:<;<7>=
04*
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Figure 7.22: Convergence of Subjdir - Learners-10 - Noisy Environment
Table 7.9: Initialisations of the Different Learners-50
Learners Direction Subjdir
Vargdir
Gendir
SVO
backward 0.9 =45/50 0.1=5/50
0.1 =5/50
forward
0.1 =5/50 0.9 =45/50 0.9 =45/50
SOV
backward 0.9 =45/50 0.9 =45/50 0.9 =45/50
forward
0.1 =5/50 0.1 =5/50 0.1=5/50
OVS
backward 0.1 =5/50 0.9 =45/50 0.9 =45/50
forward
0.9 =45/50 0.1 =5/50 0.1 =5/50
VSO
backward 0.1 =5/50 0.1 =5/50 0.1 =5/50
forward
0.9 =45/50 0.9 =45/50 0.9 =45/50
In spite of the strong initialisations, the performances of the learners are only
slightly affected by the stronger weights (table 7.10). They have performances
similar to those obtained by the learners in condition 1, as shown in figure 7.24,
comparing the learners in conditions 1 and 2.
195
58 <
8;9
9:
2 37
8 73
5 67
2 34
!
=>
" #" $ % %& #" ' ( ) (
*+-, ."."/'+10
Figure 7.23: Convergence of Subjdir - Learners-50 - Noisy Environment
Table 7.10: Convergence of the Different Learners - Condition 2
Learners Triggers
SVO-50
SOV-50
OVS-50
VSO-50
264.8
271.3
273
272
Parameters
Correct
13.5
13.5
13.5
13.5
Parameters
Set
9
9
9
9
Condition 3: Learners-10 in a Noise-free Environment
Figures 7.22 and 7.23 show some peaks in the convergence pattern displayed
by the learners. This is particularly acute in figure 7.23, where there is a fall
in the posterior probability of both the SVO and SOV learners of almost 20%
until the end of the cycle. Conditions 3 and 4 investigate how noise affects the
convergence of the learners. In this particular case, we are interested in word
196
!
!
@
? ><
=>
;
: ;<
ABDC
EFHG9GIB+JKC
" #%$
&('
$
)+*-,.
0
0
0
0
) ,. ) ,. )
*
,
.
)+*-, / * , / ) $ , / ) *-, /
*
* $ ) $
*
$
$
$
$
1+2+3546+27498
Figure 7.24: Learners’ Performances in a Noisy Environment
order noise that occurs because of incorrect directionality specifications for some
of the constituents for the target language. In order to test this, the learners are
exposed to a noise-free environment, and we compare their performances with
those obtained in the first two conditions. To obtain a noise-free environment, as
each trigger is processed a module is used for correcting category assignments if
incorrect directionality specifications are detected. This module has access to the
appropriate directionality specification of each category in English and it uses this
information to correct noisy triggers. This condition uses the same initialisations
as the ones in condition 1. The results obtained by the learners are shown in
table 7.11.
Table 7.11: Convergence of the Different Learners - Condition 3
Learners Triggers
Unset
SVO-10
SOV-10
OVS-10
VSO-10
132.13
132
128.2
131
131.5
Parameters
Correct
13.5
13.5
13.5
13.5
13.5
Parameters
Set
8
8
8.1
8
8
These learners have performances similar to those in conditions 1 and 2, with
an average of 13.5 of the 18 parameters correct in relation to the target, and
197
an average of 8 parameters that can be set with the triggers available (figure
7.25). However, the convergence is slightly faster for all learners than in the first
condition and considerably faster than in the second condition, as can be seen in
figure 7.26. These results show that, indeed, the presence of noise slows down the
convergence of the learners, because they need more triggers to compensate for the
effect produced by the noisy triggers. The declines in the posterior probabilities of
the learners in conditions 1 and 2 are caused by noise in the category assignments
of the input triggers, which provides incorrect evidence for the parameter values.
Every time a noisy trigger is encountered, it provides evidence for a non-target
parameter value, slowing down the learners.
DFEHG
IJLKMKNE+OPG
!
!
C
B A?
@A
>
= >?
0
0
0 0
)+*-,. * ) ,. ) $ ,. ) *-,. )+*-, / ) , / ) , / *1, / &('
" #%$
* * $ ) $
*
$
$ $
$
$
" #%$
465+798:6598<;
&('
$
#32
, )+*-,.
#2 #2
, ) ,. , )
* * $
$
#2 #2
,. ) , 1
* ,. ,
$
Figure 7.25: Learners’ Performances in Different Environments
Condition 4: Learners-50 in a Noise-free Environment
When the noise-free environment is used with these stronger weights, the convergence pattern is much faster for all learners, when compared to condition 2
(which uses a noisy environment), but still slower than conditions 1 and 3 (figure
7.27).
The effect produced by the noise is increased by the stronger weights, such that
all learners have a slower convergence to the target in condition 2. All the learners
have similar performances to those obtained in all the previous conditions, as can
be seen in table 7.12, and in figure 7.28, with learners which are very robust
and are converging to the target.
198
69 =
:9<
:;
3 48
9 48
6 78
3 45
"(
"'
"&
%
"$
#
"!
#)
+,.- //*0*,21
%
'*
Figure 7.26: Convergence of Subjdir - Learners-10 - Noise-free Environment
199
14 8
547
56
. /3
4 /3
1 23
. /0
!
9
:
9
" %&(' )#)#*+&-,
#
$#
Figure 7.27: Convergence of Subjdir - Learners-50 - Noise-free Environment
200
Table 7.12: Convergence of the Different Learners - Condition 4
Learners Triggers
SVO-50
SOV-50
OVS-50
VSO-50
138.5
138.5
138.5
138.5
Parameters
Correct
13.5
13.5
13.5
13.5
Parameters
Set
8
8
8
8
B
A @>
[email protected]
=
< =>
CD"E
FG7HIHJDLKE
"
"
!
1
1
1
1
+',.-/ , + -/ + & -/ + ,.-/ + , - 0 + - 0 + - 0 , - 0 ( ) $%- 2 $%- 2 $%- 2 !$- 2 $%- 2 1 $%- 2 1
#%$'&
, , & + &
,
&
+ , - / , + - / + & - / + , -/ + , - 0 + - 0
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&
&
# '$ &
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,
&
3547& 68954& 8;:
&
&
(*)
$%2 1 $%2 1 $%2
+ & -0 + , -0
&
Figure 7.28: Learners’ Performances in all the Different Environments
7.3.3
Learning in a Noisy Environment
As suggested by the results obtained in the previous experiments, noise has a
significant influence in the learning process. The next set of experiments investigates the influence of noise in the unset learner’s convergence pattern. Noise,
both in this and in the previous experiments, is related to the directionality specifications, and this corresponds to the cases where the learner is uncertain about
the thematic roles expressed in a sentence. For example, in the sentence:
• (7.8) John kisses Mary,
the learner may be uncertain as to whether it is John that is doing the kissing
action, where the logical form is:
{kiss(
1
,
2
,
3
), john(
4
,
2
), mary(
5
201
,
3
)},
or whether it is Mary and the logical form is:
{kiss(
1
,
2
,
3
), mary(
4
,
2
), john(
5
,
3
)}.
In the first case, the appropriate syntactic category for the verb has the NP
subject to the left, in S/NPo \NPs , expressing an SVO language, while in the
second the NP subject is to the right of the verb, whose category is S\NPo /NPs ,
expressing an OVS language.
If the learner chooses the second option, and the target language is English,
this sentence-logical form pair is going to provide noisy triggers for the learner,
giving evidence for another word order that does not correspond to the target
SVO. This experiment concentrates on how the convergence pattern of the learner
is going to be affected when faced with different degrees of noise introduced by
an uncertainty about thematic roles. In this case, these are incorrect triggers
for the position of the subject and the object, and they reinforce the non-target
resulting order OVS.
In this set of experiments, the unset learner is exposed to increasing levels of
noise, ranging from 10% to 50%. Sentences from the corpus are randomly selected
according to the appropriate noise level and the noise is generated by changing
the directions of the subject and object of the verb, reinforcing non-target values.
In this way, when the nosie level is 50%, it means that 50% of the sentences were
selected and were made noisy. Table 7.13 shows the performance of the unset
learner in each of these noisy environments. As indicated by these results, the
learner is robust and has a similar performance in all these environments, even
when half of the processed sentences have noise, as shown in figure 7.29. However,
the learner’s speed of convergence is strongly affected by the noise, as can be seen
in figure 7.30 for the subjdir parameter in each of these environments. There
is a significant difference in the speed of convergence that becomes slower as the
amount of noise is increased. There is a difference of up to 45% between the
noise-free case and the 50% noise case. The similar performances among the
learners are obtained due to the Bayesian framework which ensures that even
if a proportion of noisy triggers occurs during the learning process, it will not
be enough for the learner to incorrectly set its parameters permanently. Even if
the learner sets a given parameter to the non-target value due to the noise, as
long as there is a larger proportion of correct triggers, the learner will be able
to overcome this problem and re-set the parameter to the target value. In any
case, the learner is conservative and waits to set a parameter until a considerable
amount of triggers consistently gives evidence for one of the values. This ability to
deal with noise provided by the Bayesian framework proves to be very effective
in the learning process. This is an important characteristic also in terms of
human language acquisition, since it is likely to be the case that children learning
a language will be exposed to noise and ambiguity throughout the acquisition
202
process. As a consequence, they have to be able to deal with these problems
and converge to their target languages. Moreover, the environments to which the
learner is exposed are extremely noisy, with up to half of the triggers providing
evidence for another non-target language. However, even though the noise is a
burden to the learner, it does not prevent the learner from eventually setting the
parameters correctly, and converging to the target.
Table 7.13: Convergence of the Learner with Different Levels of Noise
Noise Levels
Triggers
10%
20%
30%
40%
50%
280.5
280.5
280.5
245.8
263.25
Parameters
Correct
13.5
13.5
13.5
13.5
13.5
Parameters
Set
9
9
9
9
9
!"#$%& ,-+
,*
,)
@ ,(
? >< -, '
=> +
;
: ;< *
)
(
ACB
DEACB
FGACB
HCACB
IGACB
JCACB
'
.!/
0
1243536/8790
Figure 7.29: Learner’s Performance with Different Levels of Noise
Discussion
The results obtained indicate that the different initialisations cause little impact
in the learners’ performances, in spite of delaying the convergence of those learners
that have values incompatible with the target. However, when combining the
203
+. 2
.1/
/0
( ). -)
+ ,( )*
43
563
763
463
763
463
!#" $$%!'&
Figure 7.30: Convergence of Subjdir with Different Levels of Noise
presence of noise with the use of stronger weights, there is a significant delay in
convergence, where the final posterior probability is up to 10% lower than in the
noise-free case (e.g. for the OVS learner), as can be seen in figures 7.23 and
7.27. The noise has a strong influence on the convergence of the learners, slowing
down the learning process, since the learners need more triggers to compensate
for the effect caused by the noisy ones. There is a difference of up to 45%
between the noise-free case and the 50% noise case for the unset learner. This is
a considerable difference. Nonetheless, these learners are robust, only selecting
or changing a value for a given parameter when there is strong evidence for that.
As a consequence, all the learners are converging towards the target, even with
the small amount of available triggers, regardless of the initialisations and the
presence of noise. This is the case even with an extreme bias in the initial values
(section 7.3.2), and in the presence of an extremely noisy environment (section
7.3.3). Moreover, the learners make effective use of the inheritance mechanism
to propagate default values in all the conditions.
204
7.4
Summary
In this chapter some of the tasks that the learning system has to undertake during
the learning process were discussed. The learning system starts with an incomplete grammar that has to be extended for the learner to be able to successfully
process more complex constructions. During this process, several difficulties are
encountered, and the specific case caused by the ambiguity of locative PPs was
discussed. An approach to overcome this problem was proposed, which when
adopted by the learner proved to be effective and helped the learner decide the
appropriate case for the ambiguities found in the data available. Further tests
would be necessary to analyse how well the approach would perform given a larger
amount of data and more verbs, but from the data gathered so far the proposed
approach can successfully deal with this ambiguity.
The learner uses the disambiguated input data to set the parameters of the
UG, and several models of learners were evaluated. The evaluation considered
the unset learner, and four models of default learners. They were all equally
effective in the task of acquiring word order, converging to the target grammar
given the data available. The difference between them was only in terms of the
speed of convergence, which was faster for those learners compatible or partially
compatible with the target. Nevertheless all of them were converging to the
target, regardless of the initialisations. This is the case even in the presence of
noise, which was investigated by verifying the performance of the unset learner
in environments which provided increasing levels of noise. In spite of the slower
convergence observed when the noise level was increased, even when half of the
triggers processed were noisy, the learner successfully set its parameters to the
target values. Such a learner is robust to noise and ambiguity, which are likely to
be part of the environment where children acquire their language, and it can be
used to investigate further aspects of language acquisition and potentially help
to shed light on aspects of human language acquisition.
205
Chapter 8
Conclusions and Future Work
8.1
Results and Achievements
The purpose of this research was to investigate the process of grammatical acquisition from a computational perspective, employing some ideas from Psychology
and Linguistics about human language acquisition. In order to conduct this investigation, a computational learning system, which is equipped with a model of
Universal Grammar and a learning algorithm, was implemented. Such a system
provides a robust and effective account of parameter setting, using a suitable
model of the UG, in a plausible parameter space and learning from a corpus of
parents’ spontaneous sentences to a child.
In this work we implemented a Unification-Based Generalised Categorial Grammar for English that not only served to annotate the corpus with logical forms,
but was also used as the target grammar to which the learner needed to converge. The grammar was implemented as a default inheritance network of lexical
types which resulted in a significant reduction in lexical redundancy, in an encoding that is able to describe linguistic regularities, sub-regularities and exceptions,
defined by means of typed-default feature structures. The resulting lexicon is succinctly organised and also easier to maintain and modify. This grammar is able
to capture successfully a wide range of constructions, including several different
coordination structures and unbounded dependencies.
The proposed grammatical encoding is well suited to implementing a theory
of Universal Grammar and associated principles and parameters. The UG is
represented as a UB-GCG and is embedded in a default inheritance hierarchy.
This is a clear and concise way of defining the UG with the parameters being
straightforwardly defined in the categories, in a way that makes effective use of
the default inheritance mechanism to propagate information about parameters
throughout the lexical inheritance network. The use of a default inheritance
schema to implement the UG reduced the amount of information to be acquired
by the learner, since the information was represented in a structured way. Thus
206
what is learned is not a single isolated item, but a whole structure that represents
a candidate category set and can be propagated through the hierarchies by the
inheritance mechanism. Thus the learner can use the existing hierarchies to
classify new information learned and needs only to encode the minimum amount
of arbitrary information. The proposed model of UG is consistent with typological
and linguistic ideas about the space of possible human languages. This approach
is well suited for a Principles and Parameters Theory of UG, with very general
grammar rules and categories defined as types arranged in a default inheritance
hierarchy, a kind of structure that is likely to have an important role in the way
people organise many kinds of information.
In order to provide a more realistic linguistic environment for parameter setting, a subset of the Sachs corpus, containing interactions between a child and
her parents, was annotated with logical forms. The English UB-GCG was used
to parse and annotate a subset of the Sachs corpus consisting of the parents’
sentences, with the appropriate logical forms. This corpus of child-directed transcribed speech contains a wide variety of constructions and allows us to simulate
the environment in which the child acquired her native language.
The linguistic environments to which children are exposed include a variety
of dialects and possibly more than one language, but children are robust to this
variety of influence and successfully learn those languages and dialects to which
they are consistently exposed. Sentences are produced in linguistic and nonlinguistic contexts and these are potential sources of information that children
can plausibly employ during the learning process, to minimise the problem of the
poverty of stimulus. The linguistic context was partially recreated through the
annotation of each sentence with semantic information. These environments also
exhibit statistical properties, which are a potentially useful source of information
to help learners in the task of acquiring languages on the basis of ambiguous
and noisy data. In the implemented learning system, the learner made use of
statistical information for dealing with certain ambiguities in the data, such as
that caused by locative Prepositional Phrases as arguments or adjuncts. To
resolve this ambiguity, the learner used frequency information about verbs and
locative PPs and also the idea of semantically motivated preposition selection.
This approach uses information that human language learners potentially use,
being a plausible mechanism for solving this kind of ambiguity. Another potential
use of statistical information lies in helping human language learners deal with
noise in their environment. This is incorporated in the setting of the parameters
of the UG in the learning system. The learner uses statistical information to set
the word order parameters, collecting evidence to set each parameter and only
changing the corresponding value when there is enough support in the data for
the move.
The use of categorial parameters also provides the learning system with an
incremental approach for the learning of subcategorisation frames, where the
learner is able to process categories and thus sentences, increasingly more com207
plex, given the bias of obtaining the most concise encoding consistent with the
data. Initially the learner has a restricted set of categories that it can process but,
as learning progresses, this set is expanded, with categories learned as required
by the input data.
Such a learning model presents a computationally tractable possibility for
modelling language acquisition, compatible with psychological and linguistic ideas
about human language acquisition. The learning system defined is a general computational framework that provided the possibility of exploring putative paths to
language acquisition. The learning system was used to investigate certain possibilities in the acquisition of a language, providing the necessary conditions for
performing computational simulations of the learning process. Different characterisations of learners were implemented in this framework and some aspects of
language acquisition were investigated, concentrating on the starting point for
learning and on the presence of noise in the input data. These conditions provided extreme environments for learning, but in all cases, the learners converged
towards the target grammar. The different starting points and the presence of
noise affected only convergence times, with learners further from the target having a slower convergence pattern. The learners were shown to be effective in the
language learning tasks defined, converging in the direction of the target, given
the data available. These learners were conservative and only changed a parameter after they collected enough evidence for such change. In this way, the learners
were able to deal with noise and still successfully set their parameters according
to the target even under unfavourable conditions.
As a result of implementing these ideas, we obtained a basic framework that
allows us, among other things, to perform experiments in language acquisition:
there is a plausible model of a UG with associated parameters, an English UBGCG implementing several insights into the encoding of linguistic information, a
corpus of child-directed sentences annotated with logical forms, based on which
the parameters are set and an implementation of a Bayesian learning system,
that learns in a unification-based framework. A computational learning system
like this can provide the grounds for testing the plausibility and requirements
of theories about language acquisition. Thus when a theory under investigation
does not provide the necessary conditions for a computational learner to converge
to the target, given a reasonable amount of data, then this theory is unlikely to
play an important role in human language acquisition. On the other hand, a
theory that can be successfully modelled by the learning system and that allows
the learner to converge to the target, may not reflect the way human language
acquisition occurs; it only highlights possible paths to follow. With the computational study of language acquisition, we expect to gain a better understanding
of the human language acquisition process.
The development of learning systems, such as that implemented in the scope
of this thesis, that can automatically learn linguistic information from data, opens
several possibilities for NLP systems that have traditionally been developed as
208
static and inflexible systems. The need for more adaptive technology that constantly evolves with its environment is increasing, with the necessity of dealing
with larger and larger amounts of data, which may contain noise and novel and
flexible uses of languages. Although ours is primarily a cognitive computational
model, it is potentially relevant to the development of more adaptive NLP technology.
In summary, there are seven main contributions of this enquiry. First of all, in
terms of grammar development, we integrate several ideas on the use of defaults
in linguistic description, as well as proposing novel uses of defaults, as discussed in
chapter 4. These are implemented in a Unification-Based Generalised Categorial
Grammar defined in terms of a default inheritance network of lexical types.
Secondly, we propose a plausible model of the Universal Grammar based on
typological and linguistic studies, as presented in section 4.5. We represent it
using UB-GCG, which is a formalism that has very general rules and is suited to
a description of the UG. In the proposed UG, the parameters are integrated in the
grammatical formalism, interacting with the categories and rules in the grammar.
The UG and associated parameters are embedded in a default inheritance network
of types, in a structure that is likely to have an important role in the way people
organise different kinds of information.
Thirdly, the definition of such a model of the UG embedded in a default inheritance network of types is well suited to learning purposes, since the learner can
make use of the information already represented in the grammar when acquiring
new information. This reduces the amount of information to be learned, because
when learning a new structure, the learner does not need to learn again the parts
of this new structure that are already encoded in the grammar. Thus, even if
the learner sets only a few parameters, the others will automatically have the
inherited value, even before being set by triggers. This considerably speeds up
the convergence to the target.
Fourthly, learning is defined in terms of a unification-based representation of
the UG, which allows featural variation, with categories, rules and parameters
all described in terms of feature structures. Such a grammatical representation
is suited to capturing natural languages and is consistent with recent developments in computational linguistics [Grover et al. 1993], [Sag and Wasow 1999],
[Bouma et al. in press].
Another contribution is to define learning as based on principles, such as the
Categorial Principles that were defined in CGs for independent reasons. Moreover, through the use of default inheritance hierarchies and the MDL principle,
the learning systems was able to straightforwardly learn several aspects of language, such as the linking between subcategorisation frames and predicate argument structures. Finally, the learning system implemented can successfully
learn from a corpus of real child-directed data, dealing with noise and ambiguity,
in a computational account of parameter setting that is compatible with several
characteristics of human language acquisition.
209
8.2
Future Work
Future work includes annotating more data to secure a bigger corpus, with triggers for all the parameters. This larger corpus would allow more experiments to
be conducted, testing how much data is required for all the triggers to converge
with high probability to the target grammar.
In this work, a sentence was only used to set the parameters of the UG
if the semantics for all the words in the sentence could be determined. This
research can be extended by investigating how the learner would be affected if
the semantic information it receives from the semantics learner were incomplete,
with sentences containing words for which no semantics could be determined. The
learner could benefit from using those words whose semantics could be determined
to set the appropriate parameters and this would mean more triggers for the
parameters expressed in this data, since such sentences were ignored. However,
the question is what the learner should do with the words with no semantics. One
possible solution is for the learner to try to approximate their meaning, given the
information that it may already have collected for that word. In preliminary
experiments we performed, the learner made use of the information (such as the
semantic and syntactic category) it had already collected about the words seen
so far, so that if a given word had no semantic information assigned, it used the
information it had stored about previous occurrences of the word. The results
indicated that if the word for which the semantics could not be determined had
the same part-of-speech that the one stored by the learner from previous sentences
with that word even if in a different context, the learner could minimise the
problem caused. For instance, if the semantics for eat could not be determined
for a sentence such as He ate apples, where it is a transitive verb, but the learner
has information stored from sentences containing eat as an intransitive verb, the
learner can use the information stored at least to have a better understanding of
the sentence: that He ate and that there were apples involved in the eating act.
A more thorough investigation needs to be conducted.
It is also necessary to have more resources to investigate certain aspects of
language learning, such as developmental stages. It would be desirable to have
the complete parents’ corpus annotated, to investigate how the developmental
aspects of learning would be captured by such a model. Certain phenomena
in human language acquisition occur at a later stage than others and the constructions that trigger the learning of these phenomena need to be identified in
the data. Some work has already been done in the analysis of a small number
of triggers for specific languages [Hyams 1986], but larger scale studies are still
needed. The question of the frequency of triggers should also be addressed, with
investigations of the frequency of possible triggers in child-directed data. If a
learning model requires a certain number of triggers for setting its parameters
and it is verified that the data to which children are exposed would never provide the required number, then this finding casts doubt on the plausibility of
210
such a model. Moreover, a detailed analysis of the child data and the learning
stages reflected in this data is also needed. Then a proper comparative study
could be undertaken of the developmental stages of the child during acquisition
and those of the learning system. A further development is the annotation of a
corpus of another language, preferably with a word order different from that of
English, based on which cross-linguistic comparative studies could be performed,
in relation to language acquisition in this framework. The question of learning in
a bilingual environment deserves attention and the implemented learning model
could be employed for such a task.
In summary, a better understanding of the activities and resources employed
in human language acquisition is necessary for the construction of more accurate
models of language acquisition.
211
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