INTERNATIONAL CONFERENCE ON ENGINEERING DESIGNICED 01 GLASGOW, AUGUST 21-23, 2001

A GENERAL FRAMEWORK FOR MODELING OF SYNTHESIS- INTEGRATION OF THEORIES OF SYNTHESIS Hideaki Takeda, Masaharu Yoshioka, and Tetsuo Tomiyama
Keywords: design theory, knowledge-based engineering, descriptive models of design process,abduction, model-based reasoning

1

Introduction

Engineering design consists of a variety of thought processes such as analysis, synthesis,
problem-solving, and decision-making. Among these, the most crucial process in design is“synthesis” or “synthesis-oriented thought process,” because synthesis brings about creativityof design. In spite of the importance of synthesis, compared with analysis, synthesis is lessunderstood and codified as a model.
In this paper, first we clarify the roles of synthesis in design, and then logically define design
as a synthesis-oriented thought process in a logical framework as a reasoning process. The
core part of the synthesis-oriented thought process is performed by abduction, but the overall
process is logically realized by combination of abduction and deduction. Next, synthesis andanalysis are formally distinguished.
Second, we introduce the object-dependent (or model-based) approach that has a power tonaturally represent objects in the physical world. This combination of logical and objectoriented approaches is commonly used to empower a knowledge representation scheme forthe sake of formality and expressiveness. Logic describes inter-model relations and general
operations to models, while models describe the nature of design objects and their possible
operations. We will redefine synthesis to deal with knowledge about design objects byintroducing the concept of model-based reasoning in which modeling operations performreferences to an extra-logical world in asserting logical formulae. In our formalism of
combination of logical and model-based approaches, this explicit reference to non-logicalfacts in extra-logical (i.e., model-based) world naturally integrates logic and models.
Based on this concept, we introduce and operate a variety of knowledge on objects in an
integrated way in a. reasoning framework for synthesis. The framework has the following
three features, viz., duality of abduction and deduction, multiple viewpoints, and duality oflogical and model-based reasoning. We also illustrate a prototype system of the reasoning
framework of synthesis.

2Synthesis and analysis

Synthesis can be identified in such activities as scientific discovery, design, and art including
writing novels and painting pictures. While synthesis is obviously the core of these activities,its nature is almost unclear. This chapter overviews how we deal with synthesis and defines
our approach to synthesis.
Synthesis is often counterposed to analysis and defined as an opposition of analysis, while
analysis is defined independently of synthesis. Synthesis and analysis often collocate, but thepatterns of occurrence of synthesis and analysis are different. For instance, in scientificdiscovery, synthesis very often appears after analysis. In contrast, synthesis and analysis
appear alternately and repeatedly during design.
Synthesis and analysis are also often discussed logically. A typical interpretation is thatanalysis is deductive while synthesis is non-deductive; according to Peirce [1], synthesis isoften explained by abduction. However, this correspondence might be confusing, because
analysis (or synthesis) as human activities can contain activities other than purely logicalreasoning. To clarify this, we distinguish analysis (or synthesis) as human activities fromanalysis (or synthesis) oriented thought process. Abduction and deduction are mainly used torefer to reasoning processes.

3

Logical formalization of synthesis

To logically deal with synthesis and analysis, we assume that synthesis and analysis arerational thought processes based on theories. Here a theory is a set of logical correspondence
relations (among axioms, facts, and theorems) that gives explanations for a phenomenon
described in facts based on axioms and theorems included in the theory. A thought process
based on theories is a reasoning process in which theories are used to find axioms or theorems
that explain given phenomena or to find phenomena as exemplars of axioms and theorems,
and rationality of any given process means consistency of the statement to theories.
Then, analysis and synthesis can be logically associated with deduction and abduction [2].
First, we consider the following formula.
A |- Th
This formula means that under axioms A, a set of theorems Th is proven. In this formula,finding theorems from the axioms is deduction, whereas finding axioms from given theorems
is abduction. Axioms form the basis of a theory that can explain phenomena and facts,
whereas Th consists phenomena and facts that are observed.

abduction
abduction
Fo

Fd
Fo

Fd

Fo

K
Fo
deduction

Fo
Fo

Fo

(a) Synthesis for generality

Fd

Fodeduction
Fd(b) Synthesis for individuality

Figure 1: Pattern of Process for SynthsisSince we usually have distinctions between knowledge and facts, we divide axioms into
defined facts Fd (that should be given prior to reasoning without explanation) and knowledge
K.

K ∪ Fd − Th
In contrast to Fd, we can identify facts that should appear in theorem Th and be explained.
They are called observable facts Fo. With this distinction of Fd and Fo, we can categorize
abduction more precisely.
1. Finding K and Fd from a part of Th (=Fo)
2. Finding K from a part of Th (=Fo) and Fd
3. Finding Fd from a part of Th (=Fo) and K
These three different types of abduction play their own roles in different thought processes.
For example, a scientific discovery process aims at obtaining knowledge K that should be
general and therefore minimal, while given is a part of Th (=Fo) that is individual (see Figure1(a)). Abduction in scientific discovery is types 1 or 2.Hypothetical knowledge (i.e., K)
proposed by abduction should be tested against observable facts Fo and this implies that
deduction should be performed more often than abduction.
This stands in a sharp contrast to design in which most of synthesis is abduction of type 3. In
a design process, the target is defined facts Fd that are individual, and given are knowledge K(1) Observation of phenomena
A phenomenon is observed as observations O.
(2) Extraction of facts
Observed facts Fo are extracted from O.
(3) Formation of hypotheses or selection of axioms
Fo can be used to reason out hypothetical axioms
Kh. In obvious cases, a set of known axioms Ke is
selected instead.
(4) Assuming definition facts
Initial definition facts Fd are assumed. Together
with Ke (or Kh), this will be used to derivetheorems Th. Usually, Fd contain such known facts
as boundary conditions and initial conditions.
(5) Derivation of theorems from axioms
Theorems Th are derived from Ke (or Kh) and Fd
deductively. It may break down the original
problem (i.e., derivation of theorems) into smaller
subproblems (the “divide-and-conquer strategy").
(6) Verification of theorems against facts
The derived theorems Th are tested against theobserved facts Fo to check the explicability of thetheorems. If Th ⊇ Fo, this test is satisfied. Then thetheorems are said to explain the extracted facts andthe choice of Ke (or Kh) was appropriate. If Th =Fo, then Ke is complete. If Th ⊃ Fo, then Th – Fosignifies unobserved facts or undiscovered facts inthe future or past. If Fo – Th ≠ ∅, then unexplained
facts remain.
(7) Verification of theorems against other known
axiomsThe derived theorems Th are again tested against
other known sets of axioms K’. This test verifies if
the theorems are compatible with K’ or at least if
they do not violate K’. If the hypotheses obtained instep (3) pass tests (6) and (7), they become axioms.

(a) Analysis-oriented Thought Process(1) Describing requirements
Requirements for the synthesis R are described astheorems.
(2) Extraction of requirements of interest
From R, we only focus on interesting facts as Fo.
(3) Selection of axioms
Axiom to be used is selected. Synthesis requires,various viewpoints to be considered. This means thatthe number or cardinality of K tends to be large.
(4) Derivation of solutions from requirements andaxiomsSolutions Fd are derived as facts from K and Fo.
The basic reasoning is abduction logically, but otheralgorithms to arrive at solutions can be also used.
The “divide-and-conquer strategy” might be used,
but since the number (or cardinality) of K could belarger than analysis, trade-off and negotiation among
different solutions are important.
(5) Derivation of theorems from axioms and facts
Theorems Th are derived from K and Fd deductively.
This is the same as in the analysis oriented thoughtprocess. Deduction and the divide-and-conquer
strategy are central.
(6) Verification of theorems against requirements
The derived theorems Th are tested against therequirements of interest Fo to check if the derived
Th subsume the initial requirements Fo; (i.e., Th ⊇Fo). By doing so, we can check if the solutions Fd
are satisfactory.
(7) Verification of theorems against other known
axiomsThe derived theorems are again tested against otherknown sets of axioms K’. This test verifies if Fd(and accordingly Fo) is compatible with not only K
but also K’.

(b) Synthesis-oriented Thought Process

Figure 2: Formalization of synthesis- and analysis-oriented thought processes

and observable facts Fo that is a part of Th. Abduction must be performed as many as
deduction (see Figure 1(b)), because both hypothetical facts (i.e., Fd) and observable facts(Fo) are individual. Knowledge is also different in these two processes. While minimum
knowledge K is desired in the scientific discovery process, a variety of knowledge K is
required for design, because a variety of defined facts Fd need to be found by abduction.
From the discussions above, we can now formalize the synthesis-oriented and analysis-orient
thought processes in Figure 2 [3]. While the analysis-oriented thought process (AOTP) isdeduction-dominant, the synthesis-oriented thought process (SOTP) emphasizes the role ofabduction. We can characterize SOTP in the following three dimensions in comparison withAOTP.
(1) Arbitrariness in problem definition: Enumeration of the requirements is less constraining
than observation.
(2) Arbitrariness and complexity of viewpoints: Fewer axioms are preferred in AOTP whilemore axioms are preferred in SOTP.
(3) Complicated relationship between abduction and deduction: Both AOTP and SOTP needabduction and deduction. For instance, AOTP needs abduction to form hypotheses, while
SOTP needs deduction to derive theorems in testing the facts.

Reasoning Operation(Describing Requirements,
Derivation of Solution, ..)Model Operation
Design Activities(Building, Modification, ..) (Synthesis, Analysis, ..)Design Process
Knowledge

Operation

Multiple Model-Based Reasoning

MentalWorldMediaBased

Objectdependent
modelsAbstraction
ObjectCodification

Objectindependent
model
Interpretation
Satisfiable
WFF

Representation
Real
Observation
World Abstraction
Axiom as a whole which is
the target of ontology
engineering enriches

Working Spacefor Design,
Diagnosis, etc.

metamodel
Mw ∪ GwσTh

Mwi Mw: Model
Gw i Gw: General Background Knowledge

Logical Op.

Model-based Op.

LogicalReasoning
SystemM odel-based
Reasoning Systems

Operation
Thought
processmodel(Ex.
Synthesis
OrientedThought
Process
Model)

Ontologies.

M etamodel

Th: Theorem in the Working space

Figure 3: A computational Framework of Synthesis

4

Knowledge Operations

Figure 4: Two-way Integration oflogical and model-based aspects

A computational framework for synthesis

The above discussion leads to the following two requirements for the framework to model
synthesis.
1) Explicit controls for abductive and deductive reasoning processes over facts andknowledge are needed.

2) A variety of knowledge should be provided.
We propose a computational framework of synthesis to satisfy these requirements (see Figure3). It has two main components; an object-independent model or a logical inference
workspace in which abduction and deduction are explicitly controlled, and object-dependent
models or a model-based reasoning workspace in which rich modeling knowledge is provided.
The former is introduced to satisfy the first requirement, and the latter the second. Knowledge
in a logical form has a clear syntax and therefore a sufficient computational power, but itlacks semantics that is fulfilled in real world. Model-based reasoning can offer suchknowledge that is usually difficult to describe in logic.
The logical and model-based approaches are integrated as follows (see Figure 4). First, themetamodel mechanism manages multiple model-based reasoning systems and submits
information about design objects to a common, logical workspace. This ensures smoothtransfer of design object information between logical representation and models. Second, thedesigner’s activities are represented by a set of knowledge operations that are decomposed
into logical operations and modeling operations. The logical operations operate the logicalinference workspace, while the modeling operations manipulate design object models throughthe metamodel mechanism. The multiple model-based reasoning performs assertion of logicalformula in the logical workspace. In other words, a logical formula in the logical workspace isgiven a truth value only by referring to extra-logical models, if they are satisfiable.
(Mathematically, this is called model-theoretic view as opposed to proof-theoretic view.) Thisexplicit reference to non-logical models naturally integrates logic and models.

5

Knowledge operations

This paper is based on a knowledge-centric view of design activities. We provide a set ofoperations in the knowledge level to describe designers’ activities. These knowledge
operations are decomposed into logical and modeling operations, so that they becomecomputable assuming the reasoning framework depicted in Figure 3. For example, analysis
activity is a typical use of knowledge, and activity of exchanging information with otherdesigners is a knowledge handling activity for knowledge acquisition.
As operations in the logical reasoning system, we define the following operations. First, we
provide two types of object-level reasoning based on object knowledge; i.e., (l-1) deduction ofproperties of objects from objects (design solutions), and (l-2) abduction of objects fromproperties of objects. Here, requirement specifications are included in the properties of objects.
Second, we also define meta-level reasoning as one up higher operations with operands suchas objects and properties of objects in the object level; i.e., (l-3) setting of objects, (l-4) settingof requirement specifications, (l-5) setting of design knowledge, (l-6) consistency checking of
knowledge, and (l-7) operations on the current set of design knowledge.
We provide the following eight operations as modeling operations. Among these eight, fiveoperations concern individual models; i.e., (m-1) building a model, (m-2) reasoning with themodel, (m-3) modification of knowledge, (m-4) modification of the model, and (m-5)
reference to the model. The rest three are operations for maintenance of multiple models; i.e.,(m-6) introduction of model-based systems, (m-7) selection of model-based systems, and (m8) maintenance of consistency among different models.

We define the following seven knowledge operations as combinations of logical andmodeling operations. First, to manage knowledge, there are five operations; i.e., (k-1)
knowledge/information acquisition, (k-2) knowledge/information reorganization, (k-3)
information confirmation, (k-4) conflict resolution, and (k-5) knowledge/information revision.
Second, to utilize knowledge, there are two operations; i.e., (k-6) solution synthesis and (k-7)
object analysis. Below, we describe these knowledge operations in detail.
(k-1) Knowledge/Information acquisition: The objective is to acquire knowledge andinformation related to the problem. There are two types of knowledge acquisition. One
is to introduce a knowledge source and is formalized as introducing a new modelbased system (m-6). The other is to add a new piece of knowledge to a particularmodel-based system and is formalized as modification of the knowledge base of amodel-based system (m-3). The corresponding logical operation is the operation on
the current set of design knowledge (l-7).
(k-2) Knowledge/Information reorganization: The objective is to reorganize knowledge andinformation for a task. Knowledge reorganization is a process to reorganize andmaintain a set of model-based systems that are used for a task. So, this process isformalized as selection of (one or more) model-based systems (m-7) or maintenanceof models in different model-based systems (m-8). The corresponding logicaloperation is an operation on the current set of design knowledge (l-7).
(k-3) Information confirmation: The objective is to confirm information in one knowledge
source by testing it against another information source. In this operation, the designer
confirms information in the logical level through mappings between models in theobject dependent level and the logical level. The metamodel mechanism should
provide such mappings and it is formalized as reference to the model (m-5), andsetting of design knowledge (l-5), and consistency checking of knowledge (l-6).
(k-4) Conflict resolution: The objective is to resolve conflict among different model-based
systems; for example, one modeling system says that value of an attribute of thedesign object should be 10, while another says 10.5. The logical reasoning system
detects this type of conflicts by integrating mode-based systems and solves bymodifying relationship among different mode-based systems or models in particularmodel-based systems (see k-5). It corresponds to maintenance of consistency among
different models (m-8) and consistency checking of knowledge (l-6).
(k-5) Knowledge/Information revision: The objective is to revise knowledge or information
to keep consistency with multiple models. It corresponds to modification ofknowledge in model-based systems (m-3) or modification of models (m-4), setting ofdesign knowledge (l-5) and setting of requirement specifications (l-4).
(k-6) Solution synthesis: It is synthesis in the narrow sense or abduction, i.e., to suggest a
new solution for the problem. Following SOTP in Figure 2 (b), first, the selection of
axioms for synthesis is formalized as selection of a model-based system (m-7) anddescription of the problem is formalized as building a model (m-1). Then, the designer
proposes new solution candidates by reasoning about a model (m-2). From the logicalaspect, it corresponds to setting of requirement specification (l-4), setting of design
knowledge (l-5), and abduction of objects from properties of objects (l-2).

1.

2.
3.

Derive the neighborhood system of a solution candidate from one axiom set A1.
a. Set requirements that can be treated by axioms A1 as theory (Th1) in formula (1).
i. A1' ∪F1 |-σ Th1
ii. {e1→p1,e1→p2, ..,e2→f1,e2→f2,..} ∪ F1 |-σ {p1, .., f1,..}
where ei is an abstract entity concept, pi is an attribute concept, and fi, is a function concept.
b. Derive F1={e1, e2, …} by abduction (purely logically) with the closed world assumption.
c. Analyze the neighborhood system of F1 in the attribute space and the function space by deduction usinga modeler that corresponds to Axioms A1. This will enrich Thi.
Apply previous procedures with another set of axioms and make the attribute information and function
information richer.
Compute Fn∩Fn+1∩… for narrowing the solution space to reach a solution.
Figure 5: Algorithm for model-based abduction(k-7) Object analysis: After proposing new solution candidates, the designer should test thecandidates against other knowledge sources. This operation follows AOTP shown in
Figure 2 (a). Model-based operations for this are the same to those for solution
synthesis (k-6). The difference is the reasoning mode in model-based systems, i.e.,
deductive or abductive. From the logical aspect, the first and second steps are the same
to solution synthesis (k-6), and the third step is to deduction of properties of objects (l1) instead.

6

Model-based abduction

The logical and model-based approaches are mutually integrated by knowledge operations
that can associate operations in the both workspaces. This integration enables new types ofreasoning smoothly combining different kinds of ontologies that are embedded in various
model-based reasoning systems. Here, logical level abduction is enhanced by model-based
abduction. Model-based abduction is an inference mode in which models are operated andinferred to incorporate new extra-logical statements into logical reasoning. In other words,
various knowledge bases that are based on different ontologies cooperate each other to arrive
at richer design solutions than pure logical level abduction. Model-based abduction can
provide various methods based on particular models that are used as heuristics in design suchas generate and test, catalog retrieval, case-based reasoning, computational model, andoptimization techniques instead of pure logical abduction.
The process of model-based abduction is formalized as iterative exploration of candidates byapplying different theories (see Figure 5). In order to apply this algorithm, we first needrelationships between the ontology of each model-based system and the metamodel ontology
to translate representation of a solution in one aspect to another. We also need semantic
categorization of facts into entities, functions, and properties in those ontologies to interpret
knowledge on models as formula shown in Figure 5.1.a.ii, and distribute representation of asolution into either facts or theorem. We discussed the details of model-based abduction in [4].

7Conclusions

We discussed the nature of synthesis in design and showed a model that combined both
logical and model-based representations. By doing so, we could clarify the over-all structureof the synthesis-oriented process as well as a general computational framework for modelingof synthesis that performs new types of inferences, such as knowledge integration by modelbased abduction.
Synthesis is not mere abduction but an appropriate combination of abduction and deduction.
Since actual abduction and deduction are deeply dependent on domain knowledge, we shouldmodel synthesis with knowledge operations. The proposed computational framework allows
integration of logic level reasoning and model-based reasoning that have different knowledge
bases with different ontologies.
We conducted case studies about how our framework can be applicable to actual design
processes [5][6]. We could explain core parts of the processes including analysis andsynthesis, as well as preparatory parts such as knowledge acquisition. Based on this result, weare now building a prototype system and testing it [7][8]. The system is an environment toprovide designers with various kinds of design knowledge and abductive capabilities. This
research is supported by the Research for the Future Program of the Japan Society for
Promotion of Science in the project of “Modeling of Synthesis,” JSPS-RFTF96000701
References[1]

Hartshorne, C. and Weiss, P. eds., 1931-1935, “The Collected Papers of Charles
Sanders Peirce, ” Vol. I-VI, Harvard University Press.

[2]

Takeda, H., Veerkamp, P., Tomiyama, T. and Yoshikawa, H. “Modeling design
processes”, AI Magazine, 1990, Vo.11, No. 4, pp.37-48.

[3]

Tomiyama, T., Murakami, T., Washio, T., Kubota, A., Takeda, H., Kiriyama, T.,
Umeda, Y., and Yoshioka, M., “The Modeling of Synthesis – From the Viewpoint of
Design Knowledge,” ICED ’97, 1997, pp. 97-100.

[4]

Yoshioka, M. and Tomiyama, T., “Model-based Abduction for Synthesis”, Proc. 2000
ASME Design Engineering Technical Conference & Computers and Information in
Engineering Conference, ASME, DETC2000/DTM-14553 (CD-ROM), 2000

[5]Tsumaya, A., Takeda, H. and Tomiyama, T., "A Synthesis-Related Analysis Method of
Design Protocol," ICED ’99, 1999, Vol. 3, pp. 1949-1952.

[6]

Tsumaya, A., Nomaguchi, Y., Yoshioka, M., Takeda, H., Murakami, T. and Tomiyama,T., “Verification of a Model of Synthesis -The methods for verification and results-“,
Proc. ICED 2001, (to appear)[7]

Yoshioka, M. and Tomiyama, T. “Toward a Reasoning Framework of Design as
Synthesis,” Proc. 1999 ASME International Design Engineering Technical Conferences
and Computers and Information in Engineering Conference, ASME, DETC99/DTM8743 (CD-ROM), 1999.

[8]

Yoshioka, M., Nomaguchi, Y. and Tomiyama, T, "Proposal of an Integrated Design
Support Environment Based on the Model of Synthesis", 27th Design Automation
Conference in 2001 ASME Design Engineering Technical Conference & Computers
and Information in Engineering Conference, 2001 (to appear).

Hideaki Takeda
National Institute of Informatics, 2-1-2 Hitotsubashi Chiyoda-ku Tokyo 101-8430, Japan, Tel:
+81-3-4212-2543,
Fax:+81-3-3556-1916,
E-mail:takeda@nii.ac.jp,
URL http://www-kasm.nii.ac.jp