Proceedings of DETC’03
ASME 2003 Design Engineering Technical Conferences andProceedings of DETC’03
Computers and Information in Engineering Conference
ASME 2003 Design Engineering Technical Conferences andChicago, 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: t.tomiyama@wbmt.tudelft.nl

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: takeda@nii.ac.jp

Masaharu Yoshioka
Hokkaido University
Faculty of Engineering
Kita 13, Nishi 8, Kita-ku, Sapporo 060-8628, Japan
Tel & Fax: 011-706-7107
E-Mail: yoshioka@db-ei.eng.hokudai.ac.jp

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: simomura@race.u-tokyo.ac.jp

ABSTRACT
While abduction is considered crucial for design in general,
this paper focuses on the role of abduction to integrateknowledge assuming that creative design can come frominnovative 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 showsthat abduction is indeed central to design. It also discusses thatknowledge 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 tounderstand the mechanism of design, and to formalize it with a
special focus on design knowledge. While we acknowledge theimportance 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 frominnovative, 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 theuse of a different set of knowledge that was not used forprevious design cases.
In this paper, we focus on the use of innovative, newcombination of existing, well-known knowledge. However, thismeans 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 toplay 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 thatdesign is largely a knowledge-centered activity, our previous
report [6] proposed models of analysis and synthesis (as a partof 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 researchcommunity 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 modelsof abductive reasoning. Based on his classification, this paper
tries to identify abduction that can be useful for creative design.

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The rest of the paper is organized as follows. First, we willdefine the scope, method, and approaches of the paper. Next,
we make a brief overview of abduction and introduce Schurz’sclassification of abductive reasoning [8]. We then discuss rolesof abduction in design. (In a separate report [9], we discuss acomputational method and its implementation of abduction forknowledge integration based on so-called analogicalabduction.) Then, as an example, we look at design cases ofrefrigerators. These cases will be further analyzed from theviewpoints 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 toeasily integrate knowledge, knowledge should be wellstructured and organized, by presenting some models ofknowledge 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 featuresthat 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 becalled invention to other things that are merely minor
improvement of existing designs. In addition, creativeness isrelated 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 anddesign itself is largely a knowledge-centered activity [6, 10].
Figure 1 depicts this situation in which design is a process thatconverts requirements into a design solution under someconstraints. 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 casein which the designers’ knowledge itself does not change, but
the way he/she uses it changes. Obviously they do not (orcannot) 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

DesignConstraints

DesignSolution

DesignKnowledge
Fig. 1. Knowledge-Centered View of Design

happens that they may create mental blocks that prevent themfrom 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 bringsin new design solutions. In other words, we deal with creative
design that comes from innovative, new combination ofexisting 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 ofknowledge.
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 asmorphological analysis in German design methodology [12]and TRIZ [13], define methodologies to apply design
knowledge and to arrive at creative designs more rationally andsystematically.
ABDUCTION
Deduction, Induction, and Abduction
In a traditional, simple set up, a theory consists of suchelements as axioms, facts, reasoning rules, and theorems. A
theory forms a closed domain in which a set of vocabulary isused to describe various concepts. This can be logicallyformulated 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 oftheorems. (Notice the expression A » F. Because both A and F
are sets of logical formula, the operator which signifies logicalconjunction 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 configurationof 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 isdeduction to obtain Th from A and F, while abduction obtains
F from A and Th, and induction A from F and Th1. In thisformalization, there are two important structural elements of atheory; 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 designcontext, axioms A represent design knowledge, design
procedures, physical laws, etc.; facts F represent descriptions
about design solutions; and theorems Th include properties ofdesign solutions, respectively. At the beginning of design,design requirements can be set as partial descriptions ofproperties in Th [14].
1Note that Peirce had two definitions of abduction andinduction. 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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Models of Abuductive Reasoning
Schurz [8] has compiled a (seemingly) complete model ofabduction 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 computationalalgorithms: 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 thesimplest 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 toobtainF ={C(a)}(2)
from
A = {C(x) Æ E(x)}(3)
andTh = {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 ofdesign solutions from the given design knowledge.
Law-abduction creates theoretical hypotheses and it isclosely 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 twocategories of abduction in that it generates “at least partly new
general property or natural kind of concept together with an atleast 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 andreflection 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 ofabduction is fundamental common cause abduction thatgenerates “a new unobservable property together with laws
connecting it with observable properties.” It could beformalized 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 istheoretical property abduction. In this case, from a number ofcorrelated observations, one observation seems to explain all ofthem. 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 beproduces
driven by
explained
FactualSingular
New facts
Known laws
abduction
empiricalor theories
facts↑
ObservableFactual
Known laws
fact abduction
reasons
Unobservable- ↑Unobservabl ↑fact abductione reasons↑
HistoricalFacts in the ↑
fact
past
abduction
Theoretical- ↑New initial Knownfact
or boundary theories
abduction
conditions
First
order ↑
FactualKnown laws
existential
reasons
abduction
postulating
new
unknown
individuals
Law-abduction Empirical New laws
Known laws
laws
Second order ↑New laws/ Theoretical
existential
theories with backgroundabduction
new concept knowledge↑
Micro-part
Microscopic Extrapolabduction
composition
ative
backgroundknowledge↑
Analogical
New laws/ Analogy
abduction
theories with withanalogicalbackgroundconcepts
knowledge↑
Missing-link
HiddenCausalcommoncommon
backgroundcause
causesknowledge
abduction↑
Fundamental
New
Unificationcommonunobservable of
cause
properties
backgroundabductionand laws
knowledge↑↑
TheoreticalNew
property
theoreticalabduction
entities↑↑
Abduction
External
to reality
entities
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Resistance+
CapacitanceÚ dt

Voltage

Current

dt

Inductance(b) Electric Circuit System
Mass+
Damping
Force
StiffnessÚ dt

AccelerationÚÚdtdtof abduction, obtaining formula (2), we must be given aknowledge base that contains a and a should satisfy C(a),before even we design. This means that we should know thesolution 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 byaxioms!
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 thisabduction does not directly generate design solutions, it will
generate conditions that these solutions should satisfy. In thedesign context, these conditions can become new sub design
problem or additional requirements. Therefore, it is also ofgreat 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 thefollowing 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 ofthese 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 andelasticity, 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 thesense 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 seethat factual abduction does not really lead to creative andinnovative 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, sucha mode of abduction cannot go beyond what the axioms cover
nor result in creative design. This can be seen in theformalization (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 theprevious section, abduction also plays another important role inintegrating multiple theories [6]. Given a problem and a set oftheories, if judged impossible to find a solution within thedomain, abduction can introduce an appropriate set of relevant
theories to form a new set of theories, so that solutions can befound with the new set of theories. For instance, as long as ourknowledge 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 thestrength. This is only possible when we have a piece ofknowledge that removing material that does not contribute tostrength 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 ofknowledge. In Schurz’s classification [8], this abduction for
integrating theories seems to be carried out by combination ofmodes of second order existential abduction.
For instance, we can think about the following two-stepalgorithm 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 theintegration 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, coolingtemperature and humidity, how to store and handle food, andwhere to use. Some examples of refrigerators that can be foundinclude 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 ina door, and special design for supermarkets (i.e., a box with avertical 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] torepresent 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, andTheorems 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 ofembodiment. We need a storage space that should be accessible(either from the front or from the top) and efficient enough tokeep the food cool, as well as a cooling device. Thus, we obtaintwo 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 newtheory, 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 forthese 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 ofNow, 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, and5

Copyright © 2003 by ASME

FR22: to maintain cool temperature in the storage withcool 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 anevaporator 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 theidentified enclosed, cooled storage, we need to consider
accessibility. This requires a piece of knowledge about
accessibility of human hands to an enclosed space. Ourfunctional knowledge about mechanisms tells that forhorizontal access a door and a sliding door are options, and forvertical 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 forfood 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 withcooled compartments for separate vertical access, or evenhaving 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 todemonstrate how different combinations of knowledge result indifferent 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 twopieces of knowledge.
ANALYSIS OF KNOWLEDGE USE
Following the discussions in the previous chapter, here weanalyze the refrigerator design examples more formerly. We
can indeed logically interpret these examples, using techniquesof qualitative physics, in particular, of naïve physics [17, 18].
In particular, we will focus on how different combinations ofknowledge can logically done and yield different design
solutions. This will help formalization of abduction for
integration as well.

Knowledge about CoolingFirst, let us consider design knowledge we used for
embodying FR21 with Cd (formula (15)).
TH1: An evaporator of a cooling cycle cools objects in thespace.
This sounds somewhat fundamental and might be accepted as apiece 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 heattransfer.
HT1: Heat is transferred through conduction from an
object of high temperature to one of low temperature, ifthey 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 doso, 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 atequilibrium. However, here we assume (for the sake ofsimplicity) that the heat capacity of an evaporator of a coolingcycle is sufficiently large, so that the temperature of theevaporator can remain the same, while this might not be thecase 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 Ætime (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) Æcooling_soruce(X) Ÿ temperature (X, 0°C)}(19)
FK2 = {evaporator (X) Æ cooling_soruce(X) Ÿtemperature (X, 0°C)}(20)
Now, assuming that we use air as a medium to transfer heatand that the temperature of any cooling source is substantiallybelow 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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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 thesense 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 theserequirements, we can now perform factual abduction forformula (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) Æcontact (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 thematerial, if there is a temperature difference.
IN: If a space is to be cooled efficiently, then the enclosureof the space must contain insulation.
Using these pieces of knowledge, we know that an
enclosed space with good insulation is necessary, but this ofcourse 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, logicalexpressions 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 theblocking objects to make an opening.
We also need some knowledge about “mechanisms,” suchas 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 inevery direction.
SK5: A drawer is an enclosed space with an opening forvertical 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 isused and the object can be accessed vertically.
throughSK3 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 todesign 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 coolingefficiency problem and we may arrive at a traditional
refrigerator design or one for supermarkets through factual
abduction.
Once again, abduction indeed integrated theories: inobtaining (25) and (26), we combined different kinds ofknowledge. 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 suchrather trivial theories can lead to interesting design solutions(such as refrigerators with a top opening even without a lid orwith a sliding door). In this example, we integrated heattransfer knowledge, mechanism knowledge, gas flowknowledge, heat loss and insulation knowledge, and spatial
knowledge. Some of these are relevant to each other, whilemechanism knowledge and heat transfer knowledge, forexample, 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 numberof theories available for design. This requires a further study on

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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 throughSK9 share certain concepts and form an ontology about space
and accessibility; e.g., SK1 is a super theory subsuming SK2and 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 theother hand, the design example integrated heat transfer
knowledge, gas flow knowledge, and spatial knowledge.
However, these do not share concepts and are fundamentallyirrelevant to each other. They can only be integrated, because
they dealt with an identical entity, which was, in this case, aninsulated enclosure.
This means that knowledge integration requires wellstructured and organized knowledge ready for integration. The
set-up signified by formula (1) has two important structuralelements 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 thoseelements. 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 canbe categorized as follows (see Fig. 5).
1.

2.

3.

4.

Theory 1

Theory 2(1) The axioms of the two theories areirrelevant 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 toeach other, but the concepts are sharedby 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 ofmaterials as well as a coil in circuit theory.
The two sets of axioms are irrelevant to each other, but theconcepts are shared by the two systems.
Example: Strength of materials and vibration theory sharethe identical concept of spring.
The two sets of axioms are relevant and share (at least, a
portion of) concepts.
Example: Thermodynamics and statistical mechanics sharea portion of concepts (such as temperature), but they
simply provide two different views.
The two sets of axioms are relevant; and one subsumes theother. In this case, obviously there is no need to integratetheories.
Example: The internal combustion engine is a special caseof heat engines.

Theory 1

Theory 2(3) The two sets of axioms are relevant andshare (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 beanalogical (or isomorphic) relationships among concepts. In
this case, structural similarity can help analogy, for instance,
because the same differential equation governs mechanicalvibration 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; andone subsumes the other.
Fig. 5. Relationships Between Two Theories
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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 wasonly possible, because they formed the relationships depicted inFig. 5 (1). This signifies the importance to understandknowledge structuring.
DISCUSSIONSIn the design example of refrigerator, we needed to pay a
special attention to an enclosed space with insulation addressedboth within the cooling efficiency knowledge and the spatial
knowledge. For only the storage problem, the space does noteven 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 toan enclosed space with insulation. (It is worth mentioning herethat this gradual refinement process model can indeed deal withnot 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 acommon concept, but also theories associated with properties ofthis 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, threetheories necessary for designing refrigerators are effectively
combined, viz., the cooling knowledge, the cooling efficiency
knowledge and the spatial knowledge. This combination wasnecessary to arrive at a design through factual abduction.
To design a more sophisticated refrigerator, obviously wefurther 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 thatis 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 logicalconjunctive operations, we can easily foresee problems whentheories 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 isfactual abduction to create an object that was not obvious (butcould 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 aboutknowledge structure imply that, in addition to factual andprocess 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 toimprove creativity in design.
CONCLUSIONSThis paper assumed that innovative combination ofexisting knowledge is important to arrive at new design.
Abduction is crucial not only to generate design solutions, butalso to integrate various theories about design.
Based on Schurz’s classification of abductive reasoning [8],the paper identified that abduction for integrating theories canbe 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 computationalalgorithms (although an early attempt to implement based on
analogical abduction is found in [9]). Nevertheless, it is avaluable contribution to research in abduction for design.
The paper analyzed refrigerator design cases in the form ofknowledge 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 doso.
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 boththeoretical and computational aspects. First of all, we needmore 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 agood 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 andknowledge 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 forEngineering (RACE) of the University of Tokyo for theirvaluable 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

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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.
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