Synthesis Thought Processes in Design
Hideaki Takeda
Graduate School of Information Science
Nara Institute of Science and Technology (NAIST)
8916-5, Takayama, Ikoma, Nara 630-0101, Japan
takeda@is.aist-nara.ac.jp
Akira Tsumaya
The Modeling of Synthesis Project
The University of Tokyo
Ishikawa Building 11th floor, Hongo 5-25-16, Bunkyo-ku, Tokyo 113-0033, Japan.
tsumaya@modelsyn.t.u-tokyo.ac.jp
Tetsuo Tomiyama
Research into Artifacts, Center for Engineering (RACE)The University of Tokyo
Komaba 4-6-1, Meguro-ku, Tokyo 153-8904, Japantomiyama@race.u-tokyo.ac.jp

Abstract: In this paper, we discuss what properties the synthesis process should have asa thought process and show a tentative synthesis theory. Instead of universality andminimality for knowledge for analysis, knowledge for synthesis in design needs
physicality, unlikeness, and desirability. Physicality ensures possibility of existence,
while unlikeness and desirability ensure newness, i.e., unlikeness is for ensuring that an
artifact is different from other existing artifacts, and desirability for ensuring that it hasreason to create newly. Then we show a formalization for synthesis theory that has theabove characteristics. It is based on our design process theory in which a design process
is an iterative logical process of abduction and deduction on design solution, its
properties and behaviors, and knowledge on objects. Synthesis theory for design isdefined as reconstruction process of design experiences, each of which contains thelogical design process. It consists of three steps, i.e., (1) collecting design experiences;(2) building a model that includes the collected design experiences, and (3) minimizing
an element that designers want to find newness.
Keywords: synthesis, analysis, knowledge, design, abduction

1. INTRODUCTION
In this paper, we discuss what properties the synthesis process should have as a thoughtprocess and propose a preliminary result of logical formalization of the synthesis
process.
Considering the synthesis process as a knowledge-based process, the following twoquestions are important to clarify the synthesis process; the first question is how
knowledge is used in the synthesis process, and the second one is what is knowledge forsynthesis. The first question is often mentioned as showing difference between synthesis
and analysis. One of the clearest answers is abduction proposed by C.S. Peirce [Peirce,1935]. But the second question is often missing. We tend to assume implicitly thatknowledge for synthesis is similar to knowledge for analysis. But the aims of synthesis
and analysis are so different that it is reasonable to question this assumption.
The aim of analysis is to clarify characteristics of objects. To clarify objects means
to explain different objects in the same manner. In order to apply different objects asmuch as possible, characteristics should be universal and minimum. It implies that
requirements for knowledge for analysis are also universality and minimality.
On the other hand, the aim of synthesis is to create objects having necessary
characteristics. In this case, it is not required that characteristics are universal andminimum, rather they should not be. In order to capture human desire for objects,
characteristics should be as rich as possible to represent various desires. Thus
requirements for knowledge for synthesis are not universality and minimality but rather
individuality and diversity. The last statement indicates that the assumption underlying
the traditional logical approach is not appropriate because it is to capture our world withminimum and universal axioms.
We have already proposed how synthesis can be captured in a logical frameworkthat includes abduction [Tomiyama et al., 1997] [Takeda et al., 1990a]. It is based on
logical theory, but we introduce multiple theories in a logical framework. The heart ofour formalization is that synthesis is not applying logical theories but extending andcomposing logical theories enough to represent human desire to create new artifacts. It
is denying the assumption of the traditional logical approach that we mentioned above,
but it is not clear in these papers how theories can be combined. In this paper, we extend
our formalization by including requirements for knowledge for synthesis.

AbductionP

K È Ds
Deduction
Ds1

P1

Abduction with K3
Deduction with K2

Abduction

Ds2

Ko È DsP

Abduction with K3

Ds3
P3

Deduction
Ds: Design Solution
P: Properties and Behavior of Design Solution
Ko: Knowledge on Objects
Figure 1; A Logical Framework of design process

P2

DsfinalPfinalFigure 2; Iteration of abduction anddeduction

2. THE THREE FEATURES OF DESIGNING ARTIFACTS
In the previous section, we mentioned that knowledge for synthesis is related torepresent our desires to create new artifacts. Then the question is what is necessary tocreate “new” artifacts. In other words, it is a question what conditions are required toagree that “it is new”.
We propose three features to ensure “newness” for artifacts. One is physicality that
ensures artifacts existing in the world. It is necessary for all existing artifacts that are
not even new. But it is better for designers to understand physicality because they can
use the relations between the physical characteristics to realize their intention.
Knowledge for synthesis should include knowledge for analysis in this sense. But it is
not all about knowledge for synthesis. Knowledge for analysis tends to be minimum anduniversal, while knowledge for synthesis needs much variety to represent requirements
for artifacts. It is the key issue for synthesis to provide not minimum but enoughknowledge for the given requirements.
The second feature is unlikeness, which means that it is a unique artifact. There aretwo problems in unlikeness. The first one is which set of artifacts we should take into
consideration to ensure unlikeness. It is impossible to compare the designing artifacts
with all artifacts in the world. What we can do at most is to collect artifacts that we havedesigned or encountered, learned. We call such an artifact as a design experience. We
should collect design experiences to judge unlikeness. The second problem is how tocompare the designing artifacts with others. It is often difficult to compare the designing
artifacts with some other design experience because every design experience is sodifferent in which situation we encountered it that its representation may be different
from the designing artifacts. It is the problem on ontological integration.
The third feature is desirability. Even if physicality ensures that the designing
artifact can exist in our world and unlikeness ensures that it has no similar artifacts, it is
not enough reason to realize it in our world. For example, there are no reasons to create
a new artifact that is much more complicated to the existing artifacts with the samefunctions. We need criteria to ensure that is has reasons to create new artifacts. It is avery difficult feature because most of reasons are implicit requirements from the society.
We can point out an example for it, i.e., “Occam's razor”. To make something minimize
is a good reason to create new artifacts. To minimize user operations is a good reason to
design a new consumer product.
3. REQUIREMENT FOR FORMALIZATION OF THE SYNTHESIS PROCESSIn this section, we verify our formalization of design process [Takeda et al.,1990a][Takeda et al., 1992] in the light of the above three features of the synthesis
process.
The primary formula in our formalization is the following one (see Figure 1).
Ds È Ko = P
Here Ds is a set of logical formula that represents description of design objects. P is aset of logical formula that represents description of properties of design objects. Ko is alogical formula that represents knowledge on objects. This formula means that
description of design objects with knowledge on objects can deduce description ofproperties of design objects. To keep this formula is to keep physicality condition.
The ideal design process is defined as the inference process in which description ofdesign objects can be inferred abductively from knowledge on objects and a part ofproperties of design objects as design requirements. It is not deduction process but
abduction process [Peirce, 1935].
In the actual design process, design requirements and available design knowledge
cannot be determined in advance but be defined during design. So the real design
process is defined as process repeating abduction and deduction (see Figure 2).

O3

O1
Ko1 È D1

Ko3 È D3

P1
O2
Ko2 È D2

P3

P2

O
Ko1' È D1'

Ko2' È D2'

P1'
Ko2' È D2'

P2'

P2'

(Ko1ÈKo2È ... ÈKon) È Ds?

P?

Figure 3: Integration of Design Experiences
Description of properties of design objects can be inferred deductively from descriptionof design objects and knowledge on objects. Then it can help further decision of design
requirements. Description of design objects can be inferred abductively fromdescription of properties of design objects and knowledge on objects. It can in turnsuggest what kind of knowledge is needed for the further inference.
This formalization can explain design process in a computational way and also
match the practical design processes [Takeda et al., 190b]. But the formalization has
three unsolved issues. The first one is evaluation of design solutions. Abduction process
can theoretically infer many solutions without any order 1. We need some schemes tocompare them. This issue corresponds to the desirability condition. The second is how
to provide knowledge. We assumed that knowledge could be provided a priori, but
providing knowledge is also an important process in design. The third issue, which ismore fundamental one, is how to provide representation of description of design objects,
properties of design objects, and knowledge on objects. The second and third issues
correspond to the unlikeness condition, i.e., what ontology and knowledge we should
1Some logical methods for evaluation of abduction have been proposed. For
example, to minimize propositions in hypothesis (solution) and links from hypothesis toobservation [Ng and Mooney, 1990]. But there are no reason why we should do such away.

take into consideration.
4. THE FIRST ATTEMPT TO FORMALIZE THE SYNTHESIS PROCESS
We model the synthesis process as an intended integration process of design experiences.
The basic idea is that designers can evolve not only their designing artifacts but also
their ontology and knowledge by using their design experiences. We extend ourformalization of design process to capture this process. It consist of the three processes
as follows (see Figure 3):(1) Collecting design experiences(2) Forming a model to represent the collected design experiences(3) Minimizing an element that designers want to make it new.
(1) Collecting design experiences
The issue for collecting design experiences is how to represent design experiences.
What we consider artifacts during design process means not only to remember an
artifact itself, e.g., to enumerate its attributes, but to remember or imagine what purpose
it has and why it comes to have such attributes. In other words, we can imagine its
design process. So we model a design experience as a quadruplet of Ds, Ko, P, and O,
i.e., description of design objects, knowledge on objects, properties of design objects,
and ontology to represent these three formulae respectively. We represent a set of design
experiences as
de1 = (Ds1 , Ko1 , P1 , O1 ), K, den = (Ds n , Ko n , Pn , On )Ds k È Ko k = Pk , Ds k Î Ok , Ko k Î Ok , Pk Î Ok

(1 £ k £ n )where dek denotes k-th design experience.
(2) Forming a model to represent the collected design experiences
Although we can collect a set of design experiences, they are probably based on
different ontologies so that we should integrate design experiences. It is to find a
substitution f of predicates that can map all the given ontologies O1 ... On to a single
ontology O.
de1 ' = (Ds1 ' , Ko1 ' , P1 ' , O1 ') = de1f = (Ds1f , Ko1f , P1f , O1f )K
den ' = (Ds n ' , Ko n ' , Pn ' , On ') = denf = (Ds nf , Ko nf , Pnf , Onf )O = O1f È O2f È K È Onf
Ko' = Ko1f È K È Ko nf

Table 1: A Cognitive model for case-based designStates in case-based design
The current design problem:
A design case:
The next design problem:

Formalization

Processes in case-based design
1. Adaptation of cases
1-1. modification of cases
1-2. translation of representation
2. Application of cases
2-1. change of design solution
2-1-1. use of cases
2-1-2. rejection of cases
2-2. change of design knowledge
2-3. change of specifications

Formalization(Ds, Ko, P, O )(Ds N , Ko N , PN , ON )(Ds' , Ko' , P' , O')

Ds' = f ( Ds)
Ds N ' = Dsf , Ko N ' = Ko N f , PN = PN f

Ds' = Ds È Ds N 'Ds' = Ds
Ko' = Ko È Ko N 'Ds'È Ko' = P'

The new ontology O is a base to represent the new designing objects, and new
knowledge K represents the current available knowledge.
(3) Minimizing an element that designers want to make it new.
For example, to find a simplest solution is to minimize Ds, i.e., to find Ds where
Ds < Dsk ' (1 £ k £ n ) . The other example is to find minimum knowledge. It means tofind O under the condition that Ko’ is smallest.
5. A COGNITIVE MODEL FOR CASE-BASED DESIGN
We consider how this formalization can apply actual design processes. The
straightforward application is case-based design process. Applying the formalization tocase-based design leads a new cognitive model for it.
The basic process of case-based design is iteration of recalling, adapting, andapplying cases for the current design objects. In our context, adaptation of cases consistsof two processes, i.e., modification of cases within their ontologies and translation of
their ontologies. The former includes operations like changing of parameters andconfiguration. The latter happens when we are applying cases to the design objects indifferent domains. In such cases we should map concepts in a domain to those in theother domain.
Application of cases means not only changing of the current design objects, butalso changing of knowledge and specifications. In our formalization, cases do notmeans either design objects themselves or pairs of specifications and design objects but
design experiences, i.e., sets of object properties including specifications, design objects,
and design knowledge that can reason how they are designed. When a case is applied tothe current design objects, knowledge for it is also applied to knowledge for the current
design objects. New knowledge can be valid even if the case is abandoned to apply.
New knowledge may suggest new specifications. Table 1 summaries a cognitive model
for case-based design process and correspondence to our formalization.
Some examples can be excerpted from the protocol data [Cross, 1996]. In thisprotocol, the task for design is to design a carrying device that can fasten a backpack on
the mountain bike. During the design process, the designers discussed where the device
should be located. One idea was as follows;
I: handlebars? yeah try that
J: or off this handlebar stem even because that's fixed but if it's
off the handlebars you know it's like an old bike basket that way likethe Wizard of O
K: heavy to steer tends to

The idea "old bike basket" was instantly rejected but considering this idea invokedknowledge that “power of steering bike should be reasonable”. The specification"driving a bike" now includes "good steering". In this example, the case is used as 2-1-2(rejection of case), 2-2 (change of design knowledge), and 2-3 (change of specification).
The other example is as follows;K
ooh well I've done a lot of lake touring and I've done front
panniers and I've done rear panniers and em...
Iboy that is one pannierKyeah front panniers you could you could set it up so you could haveone of these on each side there's no guarantee you'd always have two
but it's actually

The case is almost as same as the first example, i.e., "good balance is needed for drivinga bike" was introduced but the case itself was refused to use.
But the other idea that expanded to this one was suggested.
J
K
J

what if it's split
not as bad as you'd think to have just one that's off
what if the em the back backpack folds

I
K
I
J
K

they already have a hold in the middle so they could uh yeahoh like add a joint right hereyeah
so yeah so it's sorta likeso it's more like a pannier

The case was translated and then applied to the current design problem. This translation
is to extract a basic structure of "pannier" (two connecting components) and to map one
pannier to one compartment of the backpack. This use corresponds to 1-1 (modificationof cases) and 1-2 (translation of representation).
6. CONCLUSION
We show the first step of a logical formalization of the synthesis process. It is a new
approach to formalize the synthesis process in a logical framework because it can
explain how we can obtain knowledge that is often missing point when discussing
logical frameworks. But there are many unsolved problems; e.g., we could not show
how to achieve desirability. We are planning how this formalization can work in actual
design processes by testing it in protocol analysis.
ACKNOWLEDGEMENT
This research is supported by the Modeling of Synthesis Project (JSPS-RFTF 9600701)
under the Research for the Future Program of the Japan Society for the Promotion of
Science.
REFERENCES[Cross et al., 1996] Cross, N.; Christiaans, H.; Dorst, K. editors; "Analysing Design
Activities"; John Wiley & Sons, 1996
[Ng and Mooney, 1990] Ng, H.T.; Mooney; R.J.; "On the role of coherence inabductive explanation"; In Proceedings of AAAI-90, pp. 337-342, 1990
[Peirce 1935] Peirce, C.S.; "Collected Papers of Charles Sanders Peirce", volume 5;
Harvard University Press, Cambridge, MA, 1935
[Takeda et al., 1992] Takeda, H.; Tomiyama, T.; Yoshikawa, H.; "A logical andcomputable framework for reasoning in design"; In D.L. Taylor and L.A. Stauffer,
editors, Design Theory and Methodology - DTM '92 -, pp. 167-174; The American
Society of Mechanical Engineers (ASME), 1992
[Takeda et al., 1990a] Takeda, H.; Veerkamp, P.; Tomiyama, T.; Yoshikawa, H.;

"Modeling design processes"; AI Magazine, Vol. 11, No. 4, pp. 37-48, 1990
[Takeda et al., 1990b] Takeda, H.; Hamada, S.; Tomiyama, T.; Yoshikawa, H.; "A
cognitive approach of the analysis of design processes"; In Design Theory andMethodology - DTM '90 -, pp. 153-160; The American Society of MechanicalEngineers (ASME), 1990
[Tomiyama et al., 1997] Tomiyama, T.; Murakami, T.; Washio, T.; Kubota, A.; Takeda,
H.; Kiriyama, T.; Umeda, Y.; Yoshioka M.; "The modeling of synthesis -from theviewpoint of design knowledge"; In WDK 25, Proceedings of the 11th International
Conference on Engineering Design in Tampere 199, volume 3, pp. 97-100,
Tampere, Finland, 1997; Laboratory of Machine Design, Tampere University ofTechnology