The CEL Manual

The CEL Manual
The CEL Manual
Boontawee Suntisrivaraporn
Institute for Theoretical Computer Science
TU Dresden, Germany
[email protected]
Abstract
Description logics (DLs) are an important family of formalisms for reasoning
about ontologies. CEL 1 is a reasoner for the description logic EL+ , supporting
as its main reasoning task the computation of the subsumption hierarchy induced
by EL+ ontologies. The most distinguishing feature of CEL is that, unlike other
modern DL reasoners, it implements a tractable (i.e., polynomial-time) algorithm.
The supported description logic EL+ offers a selected set of expressive means that
are tailored towards the formulation of medical and biological ontologies.
Contents
1 Introduction to CEL
1
2 An Overview of CEL Ontologies
3
3 Macros and Functions
3.1 Concept and Role Construction . . .
3.2 Knowledge Base Declarations . . . .
3.3 Operations on the Ontology (TBox)
3.4 Query Commands . . . . . . . . . .
3.5 Other Commands . . . . . . . . . . .
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4 An Example: Learning by Doing
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Introduction to CEL
The description logic EL++ introduced in [1] is tailored towards the formulation of
medical and biological ontologies. A distinguishing feature of EL++ compared to other
description logics such as SHIQ and OWL [3, 4] is that, despite offering considerable
expressivity, reasoning in EL++ is tractable, i.e., can be performed in polynomial time.
1
which stands for a polynomial-time Classifier for the description logic EL+
1
This is clearly an advantage over the ExpTime worst-case complexity of reasoning in
SHIQ and OWL.
The ultimate goal of CEL is to provide a highly efficient reasoner for the description logic EL++ . A main emphasis of CEL is on reasoning with ontologies formulated
in EL++ , in particular on computing the subsumption hierarchy induced by such an
ontology. As of now, CEL implements a practically useful subset of EL++ that we call
EL+ . More precisely, EL+ provides for the following concept constructors:
• top concept “>”;
• conjunction “C u D”;
• existential restriction “∃r.C”.
For building up ontologies, the following means of expressivity are available:
• primitive concept definitions “A v D”;
• concept definitions “A ≡ D”;
• general concept inclusion (GCI) axioms “C v D”;
• concept equivalence axioms “C ≡ D”;
• transitivity assertions for roles “r ◦ r v r”;
• role hierarchy axioms “r v s”;
• right-identity rules “r ◦ s v r” and left-identity rules “r ◦ s v s”;
• role inclusion (RI) axioms of the form “r ◦ s v t”.
The ontology classification algorithm implemented in CEL has been proposed in [2].
This algorithm is a refinement for implementation purposes of the well-known polynomialtime algorithm for computing classification in EL++ giving in [1]. Currently, CEL
accepts inputs in a slight extension of the KRSS (Knowledge Representation System
Specification) syntax [5]. The following system requirements are assumed:
• Linux operating system;
• Physical memory at least 128MB.2
CEL is available as a precompiled binary package which can be run on Linux platforms.
The package can be obtained from:
http://lat.inf.tu-dresden.de/systems/cel/
2
Considerably more memory may be needed for larger ontologies.
2
The package consists of the CEL executable, this user manual, the related papers [1, 2],
and some example EL+ ontologies.
This manual details how to get CEL up and running, how to create an ontology, and
how to classify it. In Section 2, an overview of the concept and ontology language of CEL
is given. In Section 3, all commands offered by CEL will be described in detail, including
syntax and helpful examples. Finally, Section 4 gives a step-by-step introduction to
CEL at work.
2
An Overview of CEL Ontologies
Concepts and roles are built up from sets of concept and role names (which can be
freely choosen by the user), using the concept and role constructors provided by EL + .
The following syntax rules describe the formation of concepts and roles in CEL:
C −→ CN | top | (and C1 . . . Cn ) | (some RN C)
R −→ RN | (compose RN 1 RN 2 )
where CN , C, RN , and R (all possibly with subscripts) range over concept names,
concepts, role names, and roles, respectively.
A more detailed description of the syntax along with helpful examples is given in
Section 3.1.
We now give an overview of the axioms that are available for building up ontologies.
Such axioms can be devided into concept axioms and role axioms.
Primitive concept definitions state the necessary condition of a concept name.
DL notation: CN v C
CEL syntax: (define-primitive-concept CN C)
Concept definitions state the definition (both necessary and sufficient conditions) of
a concept name.
DL notation: CN ≡ C
CEL syntax: (define-concept CN C)
General concept inclusions state the subsumption (or containment) between two
concept descriptions.
DL notation: C1 v C2
CEL syntax: (implies C1 C2 )
Concept equivalence axioms state the equivalence between two concept descriptions.
DL notation: C1 ≡ C2
CEL syntax: (equivalence C1 C2 )
Role transitivity axioms assert the transitivity of a role name
DL notation: RN ◦ RN v RN
CEL syntax: (define-primitive-role RN :transitive t)
3
Role hierarchies assert the relationship between a role name and its super role name.
DL notatioin: RN 1 v RN 2
CEL syntax: (define-primitive-role RN 1 :parent RN 2 )
Right-identity (left-identity) rules specifies a right (left) identity of another role.
DL notatioin: RN 1 ◦ RN 2 v RN 1
CEL syntax: (define-primitive-role RN 1 :right-identity RN 2 ); and,
DL notatioin: RN 1 ◦ RN 2 v RN 2
CEL syntax: (define-primitive-role RN 2 :left-identity RN 1 )
Role inclusions state the subsumption (or containment) between a role composition
on the lhs and a role name on the rhs.
DL notatioin: RN 1 ◦ RN 2 v RN 3
CEL syntax: (role-inclusion (compose RN 1 RN 2 ) RN 3 )
We note that only role-inclusion and implies are sufficient to express any EL +
ontologies. The additional commands are included for ease of use and for compatibility
with other DL reasoners.
3
Macros and Functions
In this section, we give a detailes description of all commands offered by CEL. The
commands are arranged in five groups.
3.1
Concept and Role Construction
In CEL, concept and role names can be used without prior declaration. To form concept
and role names, we recommend the use of alphanumerical characters, probably including
symbols such as “ ” and “-”. Per default, CEL does not distinguish capital letters from
lower-case ones. All symbols will automatically be capitalized when processing. In case
of the need for case distinction, symbols shall be embraced within a pair of vertical
bars, that is, MALE is equivalent to Male, but |MALE| is not to |Male|.
Complex concepts and roles can be constructed using the constructors of EL + as
summarized in the grammar on Page 3. In the following, the syntax is described in
more detail.
top
keyword
Description:
Syntax:
Type:
The predefined, most general concept of any ontology, the top concept (>, aka logical truth).
top
concept constructor
4
and
keyword
Description:
Syntax:
Example:
Type:
N -ary conjunction (C1 u · · · u Cn )
(and C1 . . . Cn )
(and Human Male Drunk)
concept constructor
some
keyword
Description:
Syntax:
Example:
Remarks:
Type:
Existential restriction (∃RN .C)
(some RN C)
(some has-child Male)
Only atomic roles are allowed in an existential restriction
concept constructor
compose
Description:
Syntax:
Example:
Type:
3.2
keyword
Binary role composition (RN 1 ◦ RN 2 )
(compose RN 1 RN 2 )
(compose has-parent has-brother)
role constructor
Knowledge Base Declarations
This section introduces the commands used to build up ontologies. There are two kinds
of role axiom declarations and four kinds of concept axiom declarations.
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define-primitive-role
Description:
Syntax:
Arguments:
Example:
Remarks:
macro
Defines a role name and its properties such as its super-roles and
transitivity
(define-primitive-role RN &key (transitive nil)
(parent nil)
(parents nil)
(right-identity nil)
(left-identity nil))
RN - role name
:transitive - if set to t declares that the role name is transitive.
:parent - specifies a super-role, or alternatively, use :parents with a
singleton set, see examples.
:parents - specifies a list of super roles.
:right-identity - specifies a right-identity role for RN .
:left-identity - specifies a left-identity role for RN .
(define-primitive-role has-descendant :transitive t)
(define-primitive-role conj-role :parents (r1 . . . rn ))
(define-primitive-role cont-in :right-identity part-of)
This macro integrates several DL role axioms. As an example, we
would need two DL role axioms for the first example above: one for
the transitivity (hasDescendant ◦hasDescendant v hasDescendant)
and one for the role inclusion (hasDescendant v hasChild ). The arguments :left-identity and :right-identity are not part of the KRSS
standard.
role-inclusion
Description:
Syntax:
Arguments:
Example:
Remarks:
macro
Asserts an inclusion between a (possibly composite) role and a role
name.
(role-inclusion R RN )
R - role name or binary role composite
RN - role name
(role-inclusion has-daughter has-child)
(role-inclusion (compose has-father has-sister)
has-aunt)
This is a generalization of define-primitive-role. Role hierarchy, transitivity, and right-identity can be expressed in a more
elegant way by using define-primitive-role. This macro is not
part of the KRSS standard.
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define-primitive-concept
Description:
Syntax:
Arguments:
Examples:
Remarks:
macro
Asserts a subsumption relation between a concept name and a complex concept.
(define-primitive-concept CN C)
CN - concept name
C - (possibly complex) concept
(define-primitive-concept Father Man)
(define-primitive-concept GrandMother (and Mother
Female))
This macro states the necessary conditions for CN .
define-concept
Description:
Syntax:
Arguments:
Examples:
Remarks:
macro
Defines a concept name.
(define-concept CN C)
CN - concept name
C - (possibly complex) concept
(define-concept Father (and Man (some has-child
Human)))
This macro states both the necessary and sufficient conditions for
CN . In CEL, a concept name may have multiple definitions.
concept-inclusion , implies
Description:
Syntax:
Arguments:
Examples:
Remarks:
macro
Asserts a general concept inclusion (GCI) between two concepts.
(implies C1 C2 )
C1 , C2 - (possibly complex) concepts
(implies (and Man (some has-sibling Parent)) Uncle)
The equivalent DL notation is C1 v C2 .
equivalent
Description:
Syntax:
Arguments:
Examples:
Remarks:
macro
Asserts an equivalence between two concepts.
(equivalent C1 C2 )
C1 , C2 - (possibly complex) concept
(equivalent (and Man (some has-sibling (some has-child
Female)) (and Uncle (some has-niece top))))
The equivalent DL notation is C1 ≡ C2 .
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3.3
Operations on the Ontology (TBox)
clear-ontology , clear-tbox
Description:
Syntax:
Remarks:
macro
Removes all axioms and initializes everything.
(clear-tbox)
This macro is internally called whenever a new ontology is loaded.
load-ontology , load-tbox
Description:
Syntax:
Arguments:
Remarks:
macro
Reads in and and normalizes the input ontology.
(load-tbox tboxfile)
tboxfile - path of the input ontology file. If a filename is given
without path, the ontology is assumed to be either in the current
directory, or in the subdirectory ./tboxes.
The file specified by tbox-file is assumed to contain a list of commands as shown in Subsection 3.2. After having successfully loaded
the ontology, it is ready to be classified, see the next command.
classify-ontology , classify-tbox
Description:
Syntax:
Remarks:
macro
Classifies the loaded and normalized ontology.
(classify-tbox &key (mode 2))
Classify the current ontology depending on the mode of classification, which is defaulted to 2. In the classification mode 1, CEL
additionally computes the Hasse diagram, i.e., a directed acyclic
graph (DAG) of the terminological hierarchy. As a consequence,
classification in mode 1 usually takes longer time on the same ontology, but it also provides users with additional features thereafter.
ontology-prepared? , tbox-prepared?
Description:
Syntax:
Remarks:
macro
Checks if the ontology is prepared for classification.
(tbox-prepared?)
This is a fundamental requirement for (classify-tbox).
ontology-classified? , tbox-classified?
Description:
Syntax:
Remarks:
macro
Checks if the ontology is successfully classified.
(tbox-classified?)
This test must be positive before any subsumption queries can be
carried out.
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3.4
Query Commands
concept?
Description:
Syntax:
Arguments:
macro
Checks if the given name is known as a concept name.
(concept? CN )
CN - name to be tested
all-concepts
Description:
Syntax:
macro
Retrieves the list of all concept names occurring in the ontology.
(all-concepts)
concept-subsumes? , subsumes?
Description:
Syntax:
Arguments:
Remarks:
macro
Queries if one concept name subsumes the other.
(concept-subsumes? CN1 CN2 )
CN1 , CN2 - concept names
This macro only performs a lookup in the preclassified concept
hierarchy; it cannot be called before the test (tbox-classified?)
is positive. DL equivalent notation is CN2 v?T CN1 .
In the current version of CEL, it is not possible to query the
subsumption of complex concepts w.r.t. the classified ontology.
To perform such a subsumption query, introduce two new names
for the complex concepts in the subsumption query using defineconcept, re-classify the augmented ontology, and then use conceptsubsumes? to check subsumption between the newly introduced
concept names.
concept-implies? , implies?
Description:
Syntax:
Arguments:
Remarks:
macro
Queries if one concept name implies (is subsumed by) the other.
(concept-implies? CN1 CN2 )
CN1 , CN2 - concept names
Identical to concept-subsumes, but with swapped arguments
concept-equivalent? , equivalent?
Description:
Syntax:
Arguments:
macro
Queries if two concept names are equivalent (i.e., subsume each
other)
(concept-equivalent? CN1 CN2 )
CN1 , CN2 - concept names
9
parents
Description:
Syntax:
Arguments:
Remarks:
macro
Returns a list of direct subsumers of a concept name.
(parents CN )
CN - concept name
This feature is available only after classification in mode 1
children
Description:
Syntax:
Arguments:
Remarks:
macro
Returns a list of direct subsumees of a concept name.
(children CN )
CN - concept name
This feature is available only after classification in mode 1
ancestors , super-concepts
Description:
Syntax:
Arguments:
macro
Returns a list of all (direct and indirect) subsumers of a concept
name.
(ancestors CN )
CN - concept name
descendants , sub-concepts
Description:
Syntax:
Arguments:
macro
Returns a list of all (direct and indirect) subsumees of a concept
name.
(descendants CN )
CN - concept name
role?
Description:
Syntax:
Arguments:
macro
Checks if the given name is known as a role name.
(concept? RN )
RN - name to be tested
all-roles
Description:
Syntax:
macro
Retrieves the list of all role names occurring in the ontology.
(all-roles)
role-subsumes?
Description:
Syntax:
Arguments:
Remarks:
macro
Queries if one role name subsumes the other.
(role-subsumes? RN1 RN2 )
RN1 , RN2 - role names
DL equivalent notation is RN2 v?T RN1 .
10
role-implies?
Description:
Syntax:
Arguments:
Remarks:
macro
Queries if one role name implies (is subsumed by) the other.
(role-implies? RN1 RN2 )
RN1 , RN2 - role names
Identical to role-subsumes?, but with swapped arguments
transitive?
Description:
Syntax:
Arguments:
3.5
macro
Checks if a role name is specified as transitive.
(transitive? RN )
RN - role name
Other Commands
start
function
Description:
Syntax:
Arguments:
Remarks:
Loads, preprocesses, and classifies the ontology, all in one command.
(start tboxfile &key (mode 2)
(verbosity 2))
tboxfile - path string pointing to the input ontology file.
mode - mode of classification; when set to 1, CEL additionally computes the Hasse diagram.
verbosity - the level of verbosity CEL talks to its interactive users.
0 or nil for none, 1 for crutial messages, 2 for normal messages, t
for everything.
See load-ontology and classify-ontology.
output-subsumption
Description:
Syntax:
Arguments:
macro
Outputs all computed subsumption relationships pair by pair.
(output-subsumption [filename])
filename - file name, possibly with path, to which the subsumption
relationships are written. If not given, the output is written on the
console screen.
output-imp-sets
Description:
Syntax:
Arguments:
macro
Outputs all computed subsumption relationships in the form of
implication sets.
(output-imp-sets [filename])
filename - file name, possibly with path, to which the subsumption
relationships are written. If not given, the output is written on the
console screen.
11
output-synonyms
Description:
Syntax:
Arguments:
macro
Outputs sets of told synonyms and their representative.
(output-synonyms [filename])
filename - file name, possibly with path, to which the subsumption
relationships are written. If not given, the output is written on the
console screen.
output-hierarchy
Description:
Syntax:
Arguments:
Remarks:
macro
Outputs a visualized representation of the computed taxonomy.
(output-hierarchy [filename])
filename - file name, possibly with path, to which the subsumption
relationships are written. If not given, the output is written on the
console screen.
This feature is available only after classification in mode 1. With
large input ontologies, outputs in this format might become a mess
and could be very large.
output-hasse
Description:
Syntax:
Arguments:
Remarks:
4
macro
Outputs the computed Hasse diagram by identifying the parents
and children of each concept name.
(output-hasse [filename])
filename - file name, possibly with path, to which the subsumption
relationships are written. If not given, the output is written on the
console screen.
This feature is available only after classification in mode 1
An Example: Learning by Doing
In this section, we illustrate the use of CEL step by step. This includes
• creating an ontology,
• starting up the reasoner,
• loading the ontology,
• classifying the ontology,
• querying subsumptions, and
• output the classification.
12
Creating an Ontology CEL is a reasoning backend, and as such does not provide an
ontology editor to create and maintain ontologies. Any ontology editor that produces
KRSS syntax and supports (a subset of) the expressive means provided by EL+ can
be used together with CEL. To get started, it is perhaps advisable to generate some
simple ontologies using a standard text editor such as emacs.
The following simple ontology is provided as the file ./tboxes/med.tbox of the CEL
distribution. The concept name HDSNT is an abbreviation for “heart desease needing
treatment”.
(define-primitive-role cont-in :parent comp-of)
(implies Pericardium (and Tissue
(some cont-in Heart)))
(implies Pericarditis (and Inflammation
(some has-loc Pericardium)))
(implies Inflammation (and Disease
(some acts-on Tissue)))
(implies (and Disease
(some has-loc
(some comp-of Heart)))
(and Heartdisease
(some has-state NeedsTreatment)))
(define-concept HDSNT
(and Heartdisease
(some has-state NeedsTreatment)))
Starting up the reasoner CEL can be started by simply calling the executable in
the ./bin subdirectory of the distribution. After the reasoner has been successfully
loaded, the greeting screen will appear and CEL will prompt for commands from the
user.
Loading the ontology
At the prompt, write down the following command:
(load-ontology "med.tbox")
CEL searches for the specified ontology not only in the current directory but also in the
directory ./tboxes. A full path to the ontology file can also be given.
Classifying the Ontology After having read in and preprocessed the ontology, CEL
is ready to classify it. The user may want to check this status by asking
(ontology-prepared?)
The answer will then be t, i.e., “yes”. At this point, the classification can be started
by calling the command
13
(classify-ontology)
This may take some time depending on the size and complexity of the ontology. To
load and classify an ontology in one step, the start function can be used.
Querying Subsumption When the ontology has successfully been classified (to
check this, call (ontology-classified?)), subsumption between two concept names
w.r.t. the classified ontology can be queried. In the example ontology above, the user
might want to know if Pericarditis is in fact a heart disease needing treatment. This
can be checked by querying
(concept-subsumes? HDSNT Pericarditis).
The set of all subsumers and subsumees of a concept name can also be obtained by
using ancestors and descendants, respectively.
Output the Classification After the classification, the concept hierarchy can be
archived in a file or displayed on screen by using the functions output-subsumption
and output-imp-sets, depending on the format and brevity needed. If the classification has been carried out in mode 1, it is additionally possible with output-hasse to
output the most compact representation of a taxonomy, i.e., Hasse diagram. By using
output-hierarchy, a visualization of the terminological hierarchy can be displayed.
Moreover, (maximal) sets of pairwise subsuming concept names (called synonyms) can
be displayed by the function output-synonyms. Please refer to the more detailed explanation in Section 3.5.
References
[1] F. Baader, S. Brandt, and C. Lutz. Pushing the EL envelope. In IJCAI-05, Edinburgh, UK, 2005. Morgan-Kaufmann Publishers.
[2] Franz Baader, Carsten Lutz, and Boontawee Suntisrivaraporn. Is tractable reasoning in extensions of the description logic EL useful in practice? In Proceedings of
the 2005 International Workshop on Methods for Modalities (M4M-05), 2005.
[3] I. Horrocks, P. F. Patel-Schneider, and F. van Harmelen. From SHIQ and RDF
to OWL: The making of a web ontology language. Journal of Web Semantics,
1(1):7–26, 2003.
[4] D. L. McGuinness and F. van Harmelen. OWL web ontology language overview.
See http://www.w3.org/TR/owl-features/, 2004.
[5] P. Patel-Schneider and B. Swartout. Description-logic knowledge representation system specification from the krss group of the arpa knowledge sharing effort. Technical
report, DARPA Knowledge Representation System Specification (KRSS) Group of
the Knowledge Sharing Initiative, 1993.
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