Abduction for Creative Design
Proceedings of DETC’03
ASME 2003 Design Engineering Technical Conferences and
Proceedings of DETC’03
Computers and Information in Engineering Conference
ASME 2003 Design Engineering Technical Conferences and
Chicago, Illinois, USA, September 2-6, 2003
Computers and Information in Engineering Conference
Chicago, Illinois USA, September 2-6, 2003
DTM TOC
DETC2003/DTM-48650
DETC2003/DTM-48650
ABDUCTION FOR CREATIVE DESIGN
Tetsuo Tomiyama
Delft University of Technology
Faculty of Mechanical Engineering and Marine Technology
Mekelweg 2, 2628 CD Delft, The Netherlands
Tel: +31-15-278-1021, Fax: +31-15-278-3910
E-Mail: [email protected]
Hideaki Takeda
National Institute of Informatics
Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8430,
Japan
Tel: +81-3-4212-2543, Fax: +81-3-3556-1916
E-mail: [email protected]
Masaharu Yoshioka
Hokkaido University
Faculty of Engineering
Kita 13, Nishi 8, Kita-ku, Sapporo 060-8628, Japan
Tel & Fax: 011-706-7107
E-Mail: [email protected]
Yoshiki Shimomura
The University of Tokyo
Research into Artifacts, Center for Engineering
Komaba 4-6-1, Meguro-ku, Tokyo 153-8904, Japan
Tel: +81-3-5453-5891, Fax: +81-3-3467-0648
E-mail: [email protected]
ABSTRACT
While abduction is considered crucial for design in general,
this paper focuses on the role of abduction to integrate
knowledge assuming that creative design can come from
innovative combination of existing knowledge. Based on
Schurz’s classification of abductive reasoning, the paper
identifies that abduction for integrating theories can be
performed by a special type of abduction called second order
existential abduction. The paper then analyzes refrigerator
design cases to understand how knowledge is used and shows
that abduction is indeed central to design. It also discusses that
knowledge structure is a key concept in abduction for
integration.
Keywords: design knowledge, design reasoning, abduction,
knowledge integration, knowledge structure.
INTRODUCTION
This paper is a preliminary report on an attempt to
understand the mechanism of design, and to formalize it with a
special focus on design knowledge. While we acknowledge the
importance of generating new knowledge (such as discovery
and invention) to arrive at innovative, creative design, we also
believe that considerable cases of creative design come from
innovative, new combination of existing well-known
knowledge. In addition, giving a new set of requirements often
results in a new, creative design forcing designers to look at the
use of a different set of knowledge that was not used for
previous design cases.
In this paper, we focus on the use of innovative, new
combination of existing, well-known knowledge. However, this
means that the paper do not explain all the creative designs. It
may explain only a small portion of cases in terms of creativity,
but perhaps can do so in terms of the number of cases.
Abduction, proposed by C.S. Peirce [1, 2] is considered to
play a key role in design (e.g., see [3, 4]). Roozenburg and
Eekels [5] further proposed innoduction as a reasoning mode
more appropriate than abduction. Under an assumption that
design is largely a knowledge-centered activity, our previous
report [6] proposed models of analysis and synthesis (as a part
of design) that both include deduction and abduction. In
particular, we pointed out that abduction could be a guiding
principle for not only creation (such as design) but also
integration of superficially unrelated knowledge systems
(theories). The latter role is crucial to combine existing theories
to arrive at creative design.
Despite its importance to design, the design research
community seems to fail building full understanding of
abduction and its role in creative design. Although within both
the research communities of philosophy and AI [7], until
recently there was no comprehensive model of abduction,
Schurz [8] has seemingly succeeded in compiling such models
of abductive reasoning. Based on his classification, this paper
tries to identify abduction that can be useful for creative design.
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Copyright © 2003 by ASME
The rest of the paper is organized as follows. First, we will
define the scope, method, and approaches of the paper. Next,
we make a brief overview of abduction and introduce Schurz’s
classification of abductive reasoning [8]. We then discuss roles
of abduction in design. (In a separate report [9], we discuss a
computational method and its implementation of abduction for
knowledge integration based on so-called analogical
abduction.) Then, as an example, we look at design cases of
refrigerators. These cases will be further analyzed from the
viewpoints of knowledge used. We will discuss that the
combination of theories was actually crucial in arriving at
interesting refrigerator designs. Finally, we will argue that to
easily integrate knowledge, knowledge should be wellstructured and organized, by presenting some models of
knowledge structure.
CREATIVE DESIGN
While the purpose of the paper is not to clearly define
creative design, we discuss here the scope of the paper, i.e.,
creative design. It seems difficult, if not impossible, to define
creative design, although a reasonable way to do so is to define
it according to the characters that the design has. Creative
design exhibits functions, show performance, or have features
that existing artifacts in the category do not have and may
surprise people. However, because this definition could be
relative and subjective, it may cover something that can be
called invention to other things that are merely minor
improvement of existing designs. In addition, creativeness is
related to customer’s value or perception to a large extent.
Technological innovations do not necessarily lead to a big
commercial value.
In this paper, we regard creative design as new design and
design itself is largely a knowledge-centered activity [6, 10].
Figure 1 depicts this situation in which design is a process that
converts requirements into a design solution under some
constraints. This conversion requires design knowledge. This
formalization primarily has two possibilities to generate new
designs.
One possibility to obtain a new design happens when new
requirements and/or constraints are given even with the same
design knowledge. The other possibility happens when new
design knowledge is given. This case can be further broken
down into two cases. The first one is the case in which purely
new design knowledge is created; this may correspond to an
invention based on a new discovery. The second one is the case
in which the designers’ knowledge itself does not change, but
the way he/she uses it changes. Obviously they do not (or
cannot) use all the knowledge they have. The designers may
use a portion of knowledge that they intuitively judge relevant
for unaccountable reasons or based on past experiences. Or, it
Requirements
Design
Constraints
Design
Solution
Design
Knowledge
Fig. 1. Knowledge-Centered View of Design
happens that they may create mental blocks that prevent them
from explicitly using some knowledge, although they surely
know it if they are asked.
This paper focuses on this second case in which design
knowledge itself is known very well, but its new usage brings
in new design solutions. In other words, we deal with creative
design that comes from innovative, new combination of
existing well-known knowledge. As discussed below, the paper
will particularly discuss how to combine knowledge, but it will
not deal with the problem of how to find such a relevant set of
knowledge.
Shah [11] points out two approaches to achieve creative
designs, viz., intuitive and systematic. Intuitive approaches,
such as brainstorming, increase the flow of ideas, remove
mental blocks, and increase the chances of conditions perceived
to be promoters of creativity. Systematic approaches, such as
morphological analysis in German design methodology [12]
and TRIZ [13], define methodologies to apply design
knowledge and to arrive at creative designs more rationally and
systematically.
ABDUCTION
Deduction, Induction, and Abduction
In a traditional, simple set up, a theory consists of such
elements as axioms, facts, reasoning rules, and theorems. A
theory forms a closed domain in which a set of vocabulary is
used to describe various concepts. This can be logically
formulated as follows. A theory consists of:
A » F |-s Th
(1)
where A is a set of axioms (or rules), s is the reasoning rule
(usually modus ponens), F is a set of facts, and Th is a set of
theorems. (Notice the expression A » F. Because both A and F
are sets of logical formula, the operator which signifies logical
conjunction is a union operator ».)
Given a set of axioms (for instance, Hooke’s law) and facts
(such as Young’s modulus of steel and geometric configuration
of structure), a theory (in this case, strength of materials) can
derive theorems that explain elastic deformation of various
types of structure. Concepts in this example include such terms
as deformation, rigid bar, torsion, etc. This reasoning mode is
deduction to obtain Th from A and F, while abduction obtains
F from A and Th, and induction A from F and Th1. In this
formalization, there are two important structural elements of a
theory; i.e., axioms and concepts, which define the target
domain. In the final section of the paper about knowledge
structure, the elements of a theory and their relationships
among different theories will be further discussed
It is helpful for the reader to understand that in design
context, axioms A represent design knowledge, design
procedures, physical laws, etc.; facts F represent descriptions
about design solutions; and theorems Th include properties of
design solutions, respectively. At the beginning of design,
design requirements can be set as partial descriptions of
properties in Th [14].
1
Note that Peirce had two definitions of abduction and
induction. The explanation here is based on his early version [1,
2]. In his later version, Peirce regards abduction as a reasoning
operation more essential than induction.
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Copyright © 2003 by ASME
Models of Abuductive Reasoning
Schurz [8] has compiled a (seemingly) complete model of
abduction that classifies various types of abductive reasoning.
Table 1 shows his classification in which indentation means a
subcategory of the super. Note that his classification does not
imply clarification about all the necessary computational
algorithms: there are still many tasks to be accomplished,
although some of them can easily be implemented
computationally.
According to him, basically there are three fundamental
models of abduction; i.e., factual abduction, law-abduction,
and second order existential abduction. Factual abduction is the
simplest form of abduction in which both evidences to be
explained and abductive conjectures are always singular facts.
For example, observable-fact abduction is a reasoning to
obtain
F ={C(a)}
(2)
from
A = {C(x) Æ E(x)}
(3)
and
Th = {E(a)},
(4)
which is simply retroduction or backward reasoning (C and E
are any predicate). First order existential abduction is a special
form of this factual abduction and generates a as a variable to
be instantiated. These modes of abduction perform creation of
design solutions from the given design knowledge.
Law-abduction creates theoretical hypotheses and it is
closely related to induction. Schurz [8] explains as follows:
given a background law,
"x(C(x) Æ E(x)):
Whatever contains sugar tastes
sweet,
(5)
and an empirical law to be explained,
"x(F(x) Æ E(x)):
All pineapples taste sweet,
(6)
we may obtain
"x(F(x) Æ C(x)):
All pineapples contain sugar.
(7)
Second order existential abduction contrasts to the two
categories of abduction in that it generates “at least partly new
general property or natural kind of concept together with an at
least partly new theoretical law.” For instance, Schurz [8]
points out that analogical abduction generates a statement,
“Sound consists of atmospheric waves in analogy to water
waves,” from background laws “Laws of propagation and
reflection of water waves” and phenomenon to be explained
“Propagation and reflection of sound.”
Analogical abduction results from conceptual combination
based on isomorphic mapping. An example is shown in Fig. 2
depicting an electric circuit system and a lumped mass system.
For the both systems, an identical differential equation holds,
because there exist isomorphic mappings of system parameters
between these two systems (naturally, we need an additional
piece of mathematical knowledge about linear ordinary
differential equations).
In Schurz’s classification [8], another interesting model of
abduction is fundamental common cause abduction that
generates “a new unobservable property together with laws
connecting it with observable properties.” It could be
formalized as abduction from observed effects:
F(x) Æ G(x) (where F, G are observable properties)
(8)
to generate
F(x) Æ x has causal power PF/G(x), which produces G(x). (9)
A special kind of fundamental common cause abduction is
theoretical property abduction. In this case, from a number of
correlated observations, one observation seems to explain all of
them. Assume we have a set of propositions for some but not
all objects x:
"t(Ci(x, t) fi Ei(x, t)), 1 ≤ i ≤ n
(10)
Table 1. Classification of Abduction Modified from [8]
Abduction
Evidence Abduction
Abduction is
to be
produces
driven by
explained
Factual
Singular
New facts
Known laws
abduction
empirical
or theories
facts
↑
ObservableFactual
Known laws
fact abduction
reasons
Unobservable- ↑
Unobservabl ↑
fact abduction
e reasons
↑
HistoricalFacts in the ↑
fact
past
abduction
Theoretical- ↑
New initial Known
fact
or boundary theories
abduction
conditions
First
order ↑
Factual
Known laws
existential
reasons
abduction
postulating
new
unknown
individuals
Law-abduction Empirical New laws
Known laws
laws
Second order ↑
New laws/ Theoretical
existential
theories with background
abduction
new concept knowledge
↑
Micro-part
Microscopic Extrapolabduction
composition
ative
background
knowledge
↑
Analogical
New laws/ Analogy
abduction
theories with with
analogical
background
concepts
knowledge
↑
Missing-link
Hidden
Causal
commoncommon
background
cause
causes
knowledge
abduction
↑
Fundamental
New
Unification
commonunobservable of
cause
properties
background
abduction
and laws
knowledge
↑
↑
Theoretical
New
property
theoretical
abduction
entities
↑
↑
Abduction
External
to reality
entities
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Resistance
+
Capacitance
Ú dt
Voltage
Current
dt
Inductance
(b) Electric Circuit System
Mass
+
Damping
Force
Stiffness
Ú dt
Acceleration
ÚÚdtdt
of abduction, obtaining formula (2), we must be given a
knowledge base that contains a and a should satisfy C(a),
before even we design. This means that we should know the
solution before we design and that design boils down to search
problems or constraint solving.
Figure 3 depicts this situation. First, we are given axioms
as background knowledge and theorems as requirements.
Factual abduction generates facts that describe a design
solution. If given different requirements (i.e., a different
enclosing domain), we arrive at different design solutions.
However, these domains are already implicitly defined by
axioms!
One another important mode of abduction is theoreticalfact abduction that generates new initial or boundary conditions
that describe the yet-to-be-found design solutions. While this
abduction does not directly generate design solutions, it will
generate conditions that these solutions should satisfy. In the
design context, these conditions can become new sub design
problem or additional requirements. Therefore, it is also of
great relevance to design.
(a) Lumped Mass System
Fig. 2. Two Isomorphic Systems
in which fi means “an implication stronger than material one,
e.g., counterfactual or law-like implication.” Now assume that
“all these empirical laws are themselves correlated in the
following way”:
"x("t(Ci(x, t) fi Ei(x, t)) = "t(Cj(x, t) fi Ej(x, t))
1 ≤ i < j ≤ n.
(11)
In such a case, there must be a unifying explanation for all of
these propositions; this creates a new theory.
An example given by Schurz [8] is that “Whenever an
object exhibits conductivity of heat, it also exhibits
conductivity of electricity, characteristic flexibility and
elasticity, hardness, characteristic glossing.” Then, we might
suppose that “there is a really existing material characteristics
which is the common cause of all these empirical” propositions,
which is metallic character, M(x). We may say:
"x(M(x) = "t(Ci(x, t) fi Ei(x, t))).
(12)
From this, we actually create metallic character that unifies
those theories about behaviors such as heat conductivity,
electricity conductivity, flexibility, elasticity, etc.
Abduction for (Factual) Creation
Within the design research community, it is often pointed
out that synthesis is largely performed by abduction in the
sense of factual abduction [3, 4]. Indeed, first order existential
abduction generates an entity that performs the given
requirements. So, we name this abduction abduction for
(factual) creation.
While philosophically this analogy seems valid,
computationally (or from the design point of view), we can see
that factual abduction does not really lead to creative and
innovative design. First, it generates trivial facts from a known
set of axioms and theorem (i.e., requirements) in a domain
which is more or less covered by the axioms. In this sense, such
a mode of abduction cannot go beyond what the axioms cover
nor result in creative design. This can be seen in the
formalization (2) to (4). To computationally perform this type
Axioms
{house(X) Æhas(X, roof),
has(X, roof) Æcomfortable(X)}
Facts
{house(a)}
Theorems
{comfortable(a)}
Fig. 3. Factual Abduction
Abduction for Integration
While abduction is a crucial concept as discussed in the
previous section, abduction also plays another important role in
integrating multiple theories [6]. Given a problem and a set of
theories, if judged impossible to find a solution within the
domain, abduction can introduce an appropriate set of relevant
theories to form a new set of theories, so that solutions can be
found with the new set of theories. For instance, as long as our
knowledge is limited to the structural strength of materials of
given shape, we will never reach such an innovative design as
“drilling holes” for lighter structure while maintaining the
strength. This is only possible when we have a piece of
knowledge that removing material that does not contribute to
strength does not make any harm but only makes the whole
object lighter.
Figure 4 depicts abduction for integrating theories. First,
we are given axioms 1 as background knowledge and the
combined domain of theorems 1 and 2 as requirements (Fig. 4
(a)). However, we may notice that there is no way to arrive at
design solutions that can cover the domain designated by
(potentially) theorems 2 with only axioms 1 (hence theorems 1).
Computationally, this check can be performed by conducting
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innovative design coming from innovative combination of
knowledge. In Schurz’s classification [8], this abduction for
integrating theories seems to be carried out by combination of
modes of second order existential abduction.
For instance, we can think about the following two-step
algorithm to integrate multiple theories from different domains
(that are superficially irrelevant to each other); first to identify
the applicability and the domain of the theories to be introduced,
and second to integrate the new set of theories. The first step
identifies the relevance of the structural elements of theories,
i.e., axioms and concepts, and very much the same as
analogical abduction. The second step actually does the
integration based on, for instance, law abduction or secondorder existential abduction.
Our group has developed a prototype of a computational
tool, called Universal Abduction Studio 1 that actually
integrates different theories based on analogical abduction.
Interested readers may refer to [9].
Axioms 1
Theorems 1
Theorems 2
(a) Initial Requirements
Axioms 1
REFRIGERATOR DESIGN
To test the ideas described in the previous chapter, let us
consider a conceptual design of refrigerators [15] (this example
was inspired by [16]). While refrigerators are originally simple
devices, today we can find a variety of sophisticated designs
depending on such requirements as capacity, cooling
temperature and humidity, how to store and handle food, and
where to use. Some examples of refrigerators that can be found
include traditional design with a large compartment for normal
temperature and a freezer, advanced design with multiple
compartments including drawer-type storage and even a door in
a door, and special design for supermarkets (i.e., a box with a
vertical opening but without lid or a showcase with circulating
cool air without loosing it).
Now let us consider the most fundamental refrigerator
design which has only one cooled space. In this paper, we
employ the terminology of Suh’s axiomatic design [16] to
represent the relationships between functional requirements
(FRs) and design parameters (DPs). (Naturally, the same could
be demonstrated with other design methodologies such as [12].)
The main function requirements are:
FR1: to store food and to provide access to it, and
Theorems 1
Axioms 2
Theorems 2
(b) Incorporating Axioms 2
Axioms 1
Facts 2
Facts 1
Theorems 1
Axioms 2
FR2: to keep the food cool.
Having defined FRs in this way, we obtain a little bit of
embodiment. We need a storage space that should be accessible
(either from the front or from the top) and efficient enough to
keep the food cool, as well as a cooling device. Thus, we obtain
two DPs, viz., a storage space (S) and a cooling device (C)
resulting in the following expression. (By the way, according to
[16], this is a decoupled design that is not necessarily a good
design.)
ÈFR1˘ Èx 0˘ÈS˘
(14)
Í
˙=Í
˙Í ˙
ÎFR2˚ Îx x˚ÎC˚
Theorems 2
(c) Factual Abduction to Obtain Facts
Fig. 4. Abduction for Integrating Theories
all possible factual abduction to see if the results of abduction
cover the entire domain of theorems 1 and 2.
Results of this check may request us to incorporate a new
theory, i.e., axioms 2 that may be able to cover this domain (Fig.
4 (b)). After factual abduction using both of axioms 1 and 2, we
may arrive at facts 1 and 2 that describe a design solution for
these requirements (Fig. 4 (c)). Logically, this situation can be
represented as follows.
A1 » F |≠s Th1 » Th2
A1 » A2 » F |-s Th1 » Th2
(13)
However, notice that as a consequence of taking into
consideration additional axioms 2 besides axioms 1, we
effectively integrated axioms 1 and 2. This is an example of
Now, FR1 can be decomposed into:
FR11: to store the food in storage, and
†
FR12: to access the food in the storage.
The decomposition of FR2 depends on the embodiment, and for
instance, it can be decomposed into
FR21: to generate cool air, and
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Copyright © 2003 by ASME
FR22: to maintain cool temperature in the storage with
cool air.
The next step is embodiment. For FR11, we may need an
enclosed space (E), and for FR12 an access method to it (A).
For FR21, as working principles we may use cooling with cool
air generated by a cooling device physically realized by an
evaporator of a cooling cycle (Cd). FR22 requires thermal
conduction and insulation for the space (Tc). We may employ
other principle such as ice or radiation, but of course this will
result in another design. Consequently, we obtain the following
representation, which again is a decoupled design.
ÈFR11˘ Èx 0 0 0˘È E ˘
Í
˙ Í
˙Í ˙
(15)
ÍFR12˙ = Íx x 0 0˙Í A ˙
ÍFR21˙ Í0 0 x 0˙ÍCd˙
Í
˙ Í
˙Í ˙
ÎFR22˚ Îx 0 x x˚Î Tc˚
†
This decomposition can be continued until we identify
sufficient information regarding FRs and DPs with which we
may proceed to basic design stage. For instance, regarding the
identified enclosed, cooled storage, we need to consider
accessibility. This requires a piece of knowledge about
accessibility of human hands to an enclosed space. Our
functional knowledge about mechanisms tells that for
horizontal access a door and a sliding door are options, and for
vertical access a lid or a sliding door. We may identify a tradeoff here; having a door for horizontal access may release cooled
door, whereas doors for vertical access may not be good for
food access.
Traditional refrigerator design is to have big frontal doors
for horizontal access, which may sacrifice efficiency by loosing
cool air. More recent innovative designs include having smaller
doors instead of a single big door, drawer-like design with
cooled compartments for separate vertical access, or even
having a smaller door in the big door. If we neglect efficiency
and emphasize access, an extreme design case of a box with a
top opening without a lid that can often be seen in supermarkets
for frozen food. Another extreme is a design with frontal
sliding doors made of glass for the display purpose but with
better cooling efficiency than open box design.
These design examples do not mean, of course,
representative of creative design, but are intended to
demonstrate how different combinations of knowledge result in
different designs that can potentially be innovative. In these
design examples, the knowledge describing accessibility was
combined with the knowledge about the behavior of cooled air
for better, new designs for supermarkets. This combination
process is exactly the result of abduction to integrate these two
pieces of knowledge.
ANALYSIS OF KNOWLEDGE USE
Following the discussions in the previous chapter, here we
analyze the refrigerator design examples more formerly. We
can indeed logically interpret these examples, using techniques
of qualitative physics, in particular, of naïve physics [17, 18].
In particular, we will focus on how different combinations of
knowledge can logically done and yield different design
solutions. This will help formalization of abduction for
integration as well.
Knowledge about Cooling
First, let us consider design knowledge we used for
embodying FR21 with Cd (formula (15)).
TH1: An evaporator of a cooling cycle cools objects in the
space.
This sounds somewhat fundamental and might be accepted as a
piece of fundamental knowledge. However, below we would
like to point out that even such seemingly fundamental
knowledge is a result of combination of more fundamental
knowledge. To obtain TH1, we first need knowledge about heat
transfer.
HT1: Heat is transferred through conduction from an
object of high temperature to one of low temperature, if
they contact each other.
This can be logically formalized using first order predicate
logic as follows. Notice, however, that we may need more
carefully treatment about temporal aspects and causality; to do
so, one may use more sophisticated logic systems such as
temporal logic than standard first order predicate logic.
HT12 = {contact (A, B) Ÿ temperature (A, Ta) Ÿ
temperature (B, Tb) Ÿ Ta>Tb Æ heat_transfer (A, B)} (16)
The contact relationship is usually transitive and reflexive. So
we know:
C = {contact (A, B) Ÿ contact (B, C) Æcontact (A, C),
contact (A, B) Æ contact (B, A)}.
(17)
When heat transfer happens, the object with higher temperature
gradually cools down and the object with lower temperature
also gradually heats up, and eventually they arrive at
equilibrium. However, here we assume (for the sake of
simplicity) that the heat capacity of an evaporator of a cooling
cycle is sufficiently large, so that the temperature of the
evaporator can remain the same, while this might not be the
case for ice. In our case, after heat transfer, the object touching
the cooling source gets cooler.
HT2 = {time (T0) Ÿ heat_transfer (A, B) Ÿ evaporator
(B)
Ÿ temperature (A, Ta) Ÿ temperature (B, Tb) Ÿ Ta>Tb Æ
time (T1) Ÿ temperature (A, Tb) Ÿ T0 << T1}
(18)
In addition, we need to have knowledge about cooling sources.
Such factual knowledge about entities and their functionalities
are organized as follows [19]:
FK1 = {ice (X) Æ
cooling_soruce(X) Ÿ temperature (X, 0°C)}
(19)
FK2 = {evaporator (X) Æ cooling_soruce(X) Ÿ
temperature (X, 0°C)}
(20)
Now, assuming that we use air as a medium to transfer heat
and that the temperature of any cooling source is substantially
below normal room temperature, i.e.,
AS1 = {cooling_source (C) Ÿ temperature (C, Tc)
Ÿ food (F) Ÿ temperature (F, Tf) Ÿ Tf > Tc Ÿ air (A)
Ÿ contact (C, A) Ÿ contact (A, F)},
(21)
We now obtain from (16) to (21) our formalized knowledge:
HT1 in bold denotes a set of logical formulae, whereas
HT1 in roman typeface denotes its plain text version.
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Copyright © 2003 by ASME
HT1 » HT2 » C » FK1 » FK2 » AS1 » F |–
Th …{food (F) Ÿ temperature (F, 0°C) Ÿ time (T1)}.
(22)
Notice that the first part of formula (22) (i.e., HT1 » HT2 » C
» FK1 » FK2) denotes combination of different axioms in the
sense of Fig. 4. As a result of this combination, theorems Th
derivable from (22) now include our design requirements
(food(F) Ÿ temperature(F, 0°C) Ÿ time(T1)). From these
requirements, we can now perform factual abduction for
formula (22) and obtain
F = {evaporator (X)}
(23)
as a design solution. Even for this kind of small example, we
had to “integrate” various knowledge sources, such as HT1,
HT2, C, FK1, and FK2, by union operations (assuming that a
set union operation is equivalent to a logical conjunctive
operation). In fact, through simple forward chaining, we obtain:
HT1 » HT2 » C » FK1 » FK2 …
{evaporator (X) Æ
contact (X, A) Ÿ temperature (F, 0°C) Ÿ time (T1)}
(24)
which is equivalent to TH1.
Notice that in this simple example the knowledge
integration algorithm was not complicated (see formula (13)). It
needed forward chaining to derive (24) and second-order
existential abduction (fundamental common-cause abduction)
for the derivation of assumptions AS1 in (21), which was
accumulation of all the prerequisites in all of HT1, HT2, C,
FK1, and FK2. Further studies are needed to generalize these
operations, though.
The reasoning above does not address enclosed space,
because FR1 addresses only food storage and its accessibility.
We all know that without enclosure this design would be very
inefficient. To solve this problem, we further require
knowledge about gas flow under gravity, such as:
GF1: Under gravity, cold air sinks below warm air.
GF2: Gas flows in open space and does not flow out from a
enclosed space:
and knowledge about heat loss and insulation, such as:
HL: Heat loss inevitably happens through heat conduction,
heat radiation, or heat circulation, depending on the
material, if there is a temperature difference.
IN: If a space is to be cooled efficiently, then the enclosure
of the space must contain insulation.
Using these pieces of knowledge, we know that an
enclosed space with good insulation is necessary, but this of
course creates another problem that is accessibility; this is also
the subject of FR11 and FR12 in formula (15).
Knowledge about Space and Accessibility
Here we discuss knowledge about space and accessibility,
but for the sake of simplicity and the space reason, logical
expressions are omitted. First we discuss spatial knowledge.
SK1: Two objects cannot simultaneously occupy the same
space.
This spatial axiom can lead to a couple of other knowledge.
SK2: To move an object, a path is needed.
SK3: If a path is blocked, it can be cleared by removing the
blocking objects to make an opening.
We also need some knowledge about “mechanisms,” such
as enclosed space, door, and drawer, organized in the form of
“entity Æ property or function” [19].
SK4: An enclosed space is a space surrounded by walls in
every direction.
SK5: A drawer is an enclosed space with an opening for
vertical access, when it is open.
SK6: A horizontal door attached to an enclosed space
allows horizontal access to the space when it is open.
SK7: A vertical door attached to an enclosed space allows
vertical access to the space when it is open.
From these pieces of knowledge, based on forward
chaining, we see that
SK8: If an enclosed space has a door in front, then an
object can be horizontally taken out from the enclosed
space.
SK9: If an opening on top of an enclosed space is no
option (top surface is blocked by object), then a drawer is
used and the object can be accessed vertically.
through
SK3 Ÿ SK 6 Ÿ “direction is horizontal” |– Th … SK8.
(25)
SK3 Ÿ SK5 Ÿ “direction is vertical” Ÿ
“vertical direction should be open” |– Th … SK9.
(26)
Having this kind of knowledge (SK8 and SK9) allows us to
design an enclosed, insulated space with a door for horizontal
access (formula (25)) or with a lid or a door for vertical access
(formula (26)). This will address FR11, FR12, and the cooling
efficiency problem and we may arrive at a traditional
refrigerator design or one for supermarkets through factual
abduction.
Once again, abduction indeed integrated theories: in
obtaining (25) and (26), we combined different kinds of
knowledge. This was done by forward chaining and secondorder existential abduction as was the case for (22).
KNOWLEDGE STRUCTURE
The analysis of knowledge used in conceptual design we
discussed in the previous section showed that combining such
rather trivial theories can lead to interesting design solutions
(such as refrigerators with a top opening even without a lid or
with a sliding door). In this example, we integrated heat
transfer knowledge, mechanism knowledge, gas flow
knowledge, heat loss and insulation knowledge, and spatial
knowledge. Some of these are relevant to each other, while
mechanism knowledge and heat transfer knowledge, for
example, are irrelevant to each other. Integrating such (at least
superficially) irrelevant theories and different customer’s
requirements resulted in different design solutions.
In integrating theories, we can identify two issues that we
did not mention. One is how to identify those theories
superficially irrelevant but interesting enough to arrive at
design solutions, such as axioms 2 in Fig. 4 (b), from a number
of theories available for design. This requires a further study on
7
Copyright © 2003 by ASME
second-order existential abduction and its application to
searching candidate knowledge to be integrated.
The other issue is that we need to understand relationships
among theories. For instance, we see that theories SK1 through
SK9 share certain concepts and form an ontology about space
and accessibility; e.g., SK1 is a super theory subsuming SK2
and SK3. These pieces of knowledge have such knowledge
structure that allowed them to be integrated performed by
abduction. In fact, SK1 through SK9 has shared common
concepts, such as space, path, and object. Since SK3 is a special
case of SK1, SK3 does not even have to be integrated. On the
other hand, the design example integrated heat transfer
knowledge, gas flow knowledge, and spatial knowledge.
However, these do not share concepts and are fundamentally
irrelevant to each other. They can only be integrated, because
they dealt with an identical entity, which was, in this case, an
insulated enclosure.
This means that knowledge integration requires wellstructured and organized knowledge ready for integration. The
set-up signified by formula (1) has two important structural
elements of a theory; i.e., axioms and concepts, which define
the target domain. Thus, knowledge structure of theories boils
down to structural and ontological relationships among those
elements. Depending on these different types of relationships
among theories, algorithms or computational mechanisms of
abduction for integration can be different.
The structural relationships between these two theories can
be categorized as follows (see Fig. 5).
1.
2.
3.
4.
Theory 1
Theory 2
(1) The axioms of the two theories are
irrelevant to each other, and the concepts
used in the theories are irrelevant as well,
but they share the same entity.
Theory 2
Theory 1
(2) The two sets of axioms are irrelevant to
each other, but the concepts are shared
by the two systems.
The axioms of the two theories are irrelevant to each other,
and the concepts used in the theories are irrelevant as well,
but they share the same entity.
Example: The same entity can be a spring in strength of
materials as well as a coil in circuit theory.
The two sets of axioms are irrelevant to each other, but the
concepts are shared by the two systems.
Example: Strength of materials and vibration theory share
the identical concept of spring.
The two sets of axioms are relevant and share (at least, a
portion of) concepts.
Example: Thermodynamics and statistical mechanics share
a portion of concepts (such as temperature), but they
simply provide two different views.
The two sets of axioms are relevant; and one subsumes the
other. In this case, obviously there is no need to integrate
theories.
Example: The internal combustion engine is a special case
of heat engines.
Theory 1
Theory 2
(3) The two sets of axioms are relevant and
share (at least, a portion of) concepts.
Theory 1
In addition, even if the two sets of theories are irrelevant
and do not share any concepts, sometimes there can be
analogical (or isomorphic) relationships among concepts. In
this case, structural similarity can help analogy, for instance,
because the same differential equation governs mechanical
vibration and electrical vibration (Fig. 2). Obviously, in case of
isomorphic relationships, there is no need to integrate theories.
Besides those structural relationships among theories, we
can find ontological relationships among concepts. In Fig. 5,
we have already seen a case in which two theories sharing an
identical concept. In addition, we may have such relationships
as part-of, super-sub, and is-an-instance-of. These ontological
Theory 2
(4) The two sets of axioms are relevant; and
one subsumes the other.
Fig. 5. Relationships Between Two Theories
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Copyright © 2003 by ASME
relationships among concepts also determine the relationships
among theories, thus resulting in knowledge structure.
We can easily imagine that integration of theories becomes
an issue for cases depicted in Fig. 5 (1), (2), and (3). In the
refrigerator design case, the integration of heat transfer
knowledge, gas flow knowledge, and spatial knowledge was
only possible, because they formed the relationships depicted in
Fig. 5 (1). This signifies the importance to understand
knowledge structuring.
DISCUSSIONS
In the design example of refrigerator, we needed to pay a
special attention to an enclosed space with insulation addressed
both within the cooling efficiency knowledge and the spatial
knowledge. For only the storage problem, the space does not
even have to be enclosed. Indeed, simple shelves may suffice.
The design process was in fact a gradual refinement
process [10] and the descriptions of the solution gradually
evolved, beginning with a space, an enclosed space, and then to
an enclosed space with insulation. (It is worth mentioning here
that this gradual refinement process model can indeed deal with
not only routine design but also creative design. Basically
gradual refinement means design through synthesis-analysis
cycles and a leap in idea generation at the synthesis stage is not
excluded from the model.)
For each of this evolution (or refinement) process, a new
set of knowledge was introduced. The final solution, an
enclosed space with insulation is a fundamental common
concept obtained by fundamental common cause abduction. It
must also be mentioned that not only identifying such a
common concept, but also theories associated with properties of
this common concept is the key to fundamental common cause
abduction; i.e., identifying relevant knowledge is another key
element of this abduction.
In addition, as a consequence of this abduction, three
theories necessary for designing refrigerators are effectively
combined, viz., the cooling knowledge, the cooling efficiency
knowledge and the spatial knowledge. This combination was
necessary to arrive at a design through factual abduction.
To design a more sophisticated refrigerator, obviously we
further need to introduce other types of knowledge, such as one
about door size and cool air behavior. In case of an open top
design, we further need knowledge about customer’s needs that
is more important than efficiency.
This suggests introducing various types of knowledge
results in new design. While combining knowledge itself might
be carried out by simple set union operations or logical
conjunctive operations, we can easily foresee problems when
theories involved within theories are not ontologically related
or logically contradictory. This might be a future research issue.
Abduction has many implications to design. The first is
factual abduction to create an object that was not obvious (but
could be trivial) as a design solution. Second, it tells something
about how to organize design knowledge. From the creative
design point of view, the discussion above tells us that metalevel knowledge about relationships among different theories
together with ontological relevance of concepts is more crucial
than deeper knowledge about each of these theories.
This further has implication to design education.
Traditionally, design education was all about how to design
particular classes of artifacts. This is equivalent to teach deep
factual knowledge. Design education then focused on process
knowledge, such as design methods. The discussions about
knowledge structure imply that, in addition to factual and
process knowledge, we should teach relationships among
factual design and how to operate structured knowledge.
Deeper understanding about design knowledge structure
may improve engineering design education for the following
two reasons. First, engineering design knowledge to be learned
is increasing literally day by day. Appropriate knowledge
structuring may result in reduced factual knowledge to teach.
Second, it may help us develop a new educational method to
improve creativity in design.
CONCLUSIONS
This paper assumed that innovative combination of
existing knowledge is important to arrive at new design.
Abduction is crucial not only to generate design solutions, but
also to integrate various theories about design.
Based on Schurz’s classification of abductive reasoning [8],
the paper identified that abduction for integrating theories can
be performed by second order existential abduction. Actual
design to obtain a design solution can be performed by various
forms of factual abduction. While Schurz’s classification of
abductive reasoning is seemingly comprehensive, unfortunately
it does not contain generally applicable computational
algorithms (although an early attempt to implement based on
analogical abduction is found in [9]). Nevertheless, it is a
valuable contribution to research in abduction for design.
The paper analyzed refrigerator design cases in the form of
knowledge usage. It showed that introducing various
knowledge sources is one of the central issues of design.
Abduction for integrating theories is indeed a mechanism to do
so.
This paper reports just a beginning of on-going research
effort toward a formal computational model of design. There
are many issues to be solved in future, including both
theoretical and computational aspects. First of all, we need
more complete understanding of abductive reasoning as well as
its computational methods [7]. To integrate various knowledge
systems, the authors’ group has already proposed a mechanism
called “model-based abduction” [6].
Second, we need to clarify computational mechanisms for
abduction both for creation and for integration. In particular,
how to identify most relevant knowledge to be integrated is a
good research issue.
Third, we need to deepen understanding about knowledge
structuring, including clarification of design knowledge
structure and its computational methods. Even if design
knowledge is well-structured, knowledge acquisition and
knowledge management will be big problems to be solved.
Knowledge structuring is important not only for advanced
computational support but also for engineering design
education as suggested in the previous section.
ACKNOWLEDGEMENTS
The authors would like to thank Dr. Yutaka Nomaguchi
and Hiromitsu Sakai of Research into Artifacts, Center for
Engineering (RACE) of the University of Tokyo for their
valuable inputs in the early stage of the research. The authors
would like also to thank Prof. Klaas van der Werff, Bart Meijer,
and Bart van der Holst at Faculty of Mechanical Engineering
9
Copyright © 2003 by ASME
and Marine Technology of Delft University of Technology for
their contributions especially to the analysis of refrigerator
design. This research was partially supported by the Ministry of
Education, Science, Sports and Culture of Japan, Grant-in-Aid
for Scientific Research (B)(1), 14380170, 2002.
REFERENCES
[1] Hartshorne, C., and Weiss, P. eds., 1931-1935, The
Collected Papers of Charles Sanders Peirce, Vol. I-VI,
Harvard University Press, Cambridge, MA.
[2] Burks, A., ed., 1958, The Collected Papers of Charles
Sanders Peirce, Vol. VII-VIII, Harvard University Press,
Cambridge, MA.
[3] Coyne, R., 1988, Logic Models of Design, Pitman,
London.
[4] Yoshikawa, H., 1989, “Design Philosophy: The State of
the Art,” Annals of the CIRP, 38/2, pp. 579-586.
[5] Roozenburg,
N.F.M.,
and
Eekels,
J.,
1995,
Product Design: Fundamentals and Methods, John Wiley
& Sons Chichester, MA.
[6] Takeda, H., Yoshioka, M., and Tomiyama, T., 2001, “A
General Framework for Modelling of Synthesis –
Integration of Theories of Synthesis,” in Proceedings of
ICED ’01, pp. 307-314.
[7] Flach, P.A., and Kakas, A.C., 2000, “Abductive and
Inductive Reasoning: Background and Issues,” in Flach,
P.A., and Kakas, A.C., eds., Abduction and Induction:
Essays on Their Relation and Integration, Kluwer
Academic Publishers, Dordrecht, pp. 1-27.
[8] Schurz, G., 2002, Models of Abductive Reasoning,
TPD Preprints Annual 2002 No. 1, Schurz G. and
Werning, M., eds., Philosophical Prepublication
Series of the Chair of Theoretical Philosophy at the
University of Düsseldorf, (http://service.phil-fak.uniduesseldorf.de/ezpublish/
index.php/article/articleview/70/1/14/), to appear in
Synthese (Kluwer Academic Publishers, Dordrecht),
in 2003.
[9] Takeda H., Sakai H., Nomaguchi Y., Yoshioka M.,
Shimomura Y., and Tomiyama T., 2003, “Universal
Abduction Studio–Proposal of a Design Support
Environment for Creative Thinking in Design–,” to appear
in Proceedings of ICED ’03.
[10] Tomiyama, T., 1995, “A Design Process Model that
Unifies General Design Theory and Empirical Findings,”
in Ward, A.C., ed., Proceedings of the 1995 Design
Engineering Technical Conferences, DE-Vol. 83,
ASME, New York, pp. 329-340.
[11] Shah, J., 1998, “Experimental Investigation of Progressive
Idea Generation Techniques,” in Proceedings of the 1998
Design Engineering Technical Conferences (CD-ROM),
DETC98/DTM-5676, New York, ASME.
[12] Pahl, G., and Beitz, W., 1996, Engineering Design:
Systematic Approach, Berlin, Springer-Verlag, 2nd
revised edition ed. Wallace, K.
[13] Altshuller, G., 1999, The Innovation Algorithm; TRIZ,
Systematic Innovation and Technical Creativity,
Worcester, MA, Technical Innovation Center.
[14] Takeda, H., Veerkamp, P., Tomiyama, T., and
Yoshikawa, H., 1990, “Modeling Design Processes,” AI
Magazine, 11/4, pp. 37-48.
[15] Meijer B.R, Tomiyama T., van der Holst B.H.A.,
and van der Werff K., 2003, “Knowledge
Structuring for Function Design,” to appear in CIRP
Annals, 52/1.
[16] Suh, N.P., 1990, The Principles of Design, Oxford
University Press, Oxford, New York.
[17] Hayes, P.J., 1985, “The Second Naive Physics
Manifesto,” in Hobbs, J.R., and Moore, R.C., eds., Formal
Theories of the Commonsense World, Ablex Publishing
Corp., Norwood, NJ., pp. 1-36.
[18] Hayes, P.J., 1985, “Naive Physics Manifesto I: Ontology
for Liquids,” in Hobbs, J.R., and Moore, R.C., eds.,
Formal Theories of the Commonsense World, Ablex
Publishing Corp., Norwood, NJ., pp. 71-107.
[19] Takeda, H., Hamada, S., Tomiyama, T., and Yoshikawa,
H., 1990, “A Cognitive Approach to the Analysis of
Design Processes,” in Rinderle, J.R., ed., Design Theory
and Methodology –DTM '90–, DE-Vol. 27, ASME, New
York, pp. 153-160.
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