A Philosophical Foundation of Qualitative Modeling MethodologiesBased on the Yin-Yang Principle

Abstract

In this paper, we develop a philosophical foundation forqualitative modeling and reasoning methodologies . First, weintroduce the Yin and Yang principle and briefly review itsorigins in Chinese philosophy . We analyze the classical Westernscience model from a Yin-Yang perspective, and compareEastern and Western approaches to methods of scientificinquiry. We show that traditional dichotomies such as hardversus soft sciences, quantitative-formal versus qualitative-informal methods, or objective versus subjective perspectivesbreak down in light of modern scientific discoveries . We arguethat qualitative modeling and reasoning may provide anintegrative methodological framework that overcome those rigidlimitations . We point out several properties of qualitativereasoning methods and applications that bear closerrelationships to Eastern philosophical principles than to thetraditional model of Western science . We relate some majorassumptions, features and characteristics of qualitative modelingand reasoning to Yin-Yang theory and show that Easternthought can contribute significantly to the motivation andunderstanding of qualitative reasoning as a particular scientificmethod .

IntroductionWestern thought and philosophical approaches have laidthe foundation of most scientific disciplines and domainsin the 19th century and continue to dominate scientificmethodologies in many areas . Originating in the sciences,especially in physics, the Cartesian or Newtonianworldview has shaped scientific paradigms in terms ofproblem identification, problem definitions, problemdescription and modeling, and problem solving methods .Adopting scientific principles like objectivity,reductionism, and deterministic modeling andclassification has helped advancing the sciences into themodem age and building engineering devices and artifactsof increasing complexity and utility . However, thismechanistic worldview is now increasingly showing itslimitations in the understanding and mastering of intricatereal-world phenomena . Modern science across alldisciplines is beginning to see a certain paradigm shift

QR99 Loch Awe, Scotland

Weiyin Hong and Karl R. Lang

Department ofInformation and Systems ManagementHK University ofScience & Technology (HKUST), Hongkong

Tel: +852.2358.7633, Fax: +852.2358.2421Email : (hongwy, klang)@ust.hk

moving towards a new worldview that emphasizesconcepts like uncertainty, imprecision, dynamics, process-orientation, qualitativeness, and multi-perspective,holistic thinking .Yin-Yang theory is the core of Chinese philosophy,

reflecting the basic view of the world by Chinese peoplefor over two thousand years (Yang 1993, Xu 1995, Zhu1992) . As a comprehensive theory, it includes themechanism of Yin-Yang, the tool of Eight-Hexagrams,and the symbol of T'ai-Chi, which as a whole representsChinese people's conception about the nature, the originand development of the world . Such an insight into theintrinsic mechanism of the universe as well as the effort toput the idea into practice once put China ahead ofWestern countries in scientific advancement in boththeory, technology, and cultural development .

Supported by the great scientific discoveries byscholars like Kepler (1571-1630) and Galileo (1564-1642), the metaphysical world view of the medieval timeswas gradually replaced by the modern scientificorientation developed and formulated by Descartes (1596-1650) and Newton (1642-1727). Originating in thesciences, especially in physics, the Cartesian orNewtonian worldview has shaped scientific paradigms interms of problem identification, problem definitions,problem description and modeling, and problem solvingmethods. Adopting scientific principles like objectivity,reductionism, and deterministic modeling andclassification has helped advancing the sciences into themodern age, and eventually led to the IndustrialRevolution characterized by engineering projects ofunprecedented scale and complexity . However, thismechanistic worldview is now increasingly showing itslimitations in the understanding and mastering of intricatereal-world phenomena . Modern science across alldisciplines is beginning to see a certain paradigm shiftmoving towards a new worldview that emphasizesconcepts like uncertainty, imprecision, dynamics, process-orientation, qualitativeness, and multi-perspective,holistic thinking (Capra 1988) .

128

We argue that although seemingly different, theWestern and Eastern approaches are basically differentways of tackling the same problem, that is, we caninterpret modern science in the language of Yin-Yangtheory, and thus suggest a new paradigm by incorporatingEastern philosophy into the Western science model . In thefield of computer science, for example, Sodan (1998) hasshown evidence of the correspondence between Yin/Yangtheory and certain CS concepts and methods, and claimedthat the integration of both qualities offers the prospect ofsolving more complex problems . In another piece of Alresearch, Minsky (1991) also proposed that AT researchmust now move from its traditional focus on particularschemes to an integration of modular learning machineswith common sense knowledge reservoir. Specifically, weargue that Qualitative Reasoning could be seen as aparticular example of such an integrative and hybridframework .

In Section 2, the authors will introduce the concept andphilosophy of Yin-Yang theory, and explain them in thelight of its applicability in Western science. In Section 3,the focus of our paper, we will analyze the relationshipbetween qualitative modeling methods and Yin-Yangtheory, and propose an integrative framework for itsdevelopment. In Section 4, we will conclude the paperwith a discussion and point out some limitations of thispaper.

Yin-Yang Theory and Modern Science

Origin and Concept of Yin-YangFirst appeared in I-ching, the concept of Yin-Yang datesback to the Xia Dynasty around 2205 B.C . (Lu 1990) . Itoriginated from the observation of real world phenomena,where there always exist pairs of opposite yet relatedobjects or concepts (Table 1) .

Objects

Properties

Table 1 : Yin-Yang Pairs as Real Objects andProperties (Capra 1988, p.36)

Yin-Yang is a highly abstract yet very common term . Itrepresents the common characteristic or status of almostall things rather than a particular object (Xu D. Y . 1995P.29) . In Lao-Tzu, an ancient Chinese scripture, theconcept of Yin-Yang is further abstracted into a higher

QR99 Loch Awe. Scotland

conceptual level . It is seen as opposite properties of thesame thing, or the relative relationship between twothings (Yang X. P. 1993) .

Ubiquity of Yin/Yang Dichotomic PairsPrinciple 1 : Everything in the world has both Yin andYang properties (ubiquity) . There is no absolute Yin orYang existing (relativity) . A harmonious combination ofthese two properties is always preferred over pureemphasis on either ofthem .

Chinese people believe that the world itself is createdby the interaction of two opposite forces, Yin and Yang,and therefore everything in the world has both properties .Neither of them can exists alone (Lu 1990), such as"cold" and "hot", "good" and "bad" . We can easily findsuch dichotomic pairs in the symbolic system of modemscience as well (Table 2) .

Table 2 : Yin-Yang Pairs ofScientific Symbolic SystemNot only the symbolic system of western modern

science is consistent with Yin-Yang concept, thedifference between Eastern and Western science can alsobe explained by Yin-Yang theory . "Science" can bedefined as a process of inquiry, inquiry into a body ofknowledge and the process which generates newknowledge (Ackoff, 1962) . However, the approach ofmaking such inquiry is quite different in Eastern andWestern scientific approaches (Table 3) .As we can see from the table that the Eastern science

approach starts out with abstract concepts about the natureof the world, whereas Western science is foremost basedon empirical observations (Ciborra 1998) . The twoapproaches themselves can be captured as a dichotomicpair, each having its own power and weakness . While theEastern approach (Yin) has the strength of capturing theprinciples of the world, it generally lacks explicitlyprescribed operational procedures . On the other hand, theWestern approach (Yang) is powerful at directingempirical application but prone to theoreticalfragmentation . Now, deriving from Yin-Yang theoryitself, we may achieve better results if we can

inn

2

Yin Yan s,,Mathematics negative (-) positive (+)

odd evenComputer analog digitalScience asynchronous synchronousPhysics counter-force force

negative positiveelectron electron

Methodology qualitative quantitativebottom-up top-downtheoretical emvirical

Philosophy falsehood truthinductive deductivedescriptive normative

Yin- -

1 YangEarth HeavenMoon SunFemale MaleNight DayWinter SummerInterior SurfaceCoolness Warmth

ResponsiveI

AggressiveIntuitive Rational

appropriately combine these two approaches into aharmonious one, that is, let both of them make a movetowards each other.

EasternApproach

Ahstract and intrinsic law of nature

Concrete real world phenomena & dataFigure 1 . The Framework ofEastern versus

Western Approaches

Nested Nature of Yin/Yang Dichotomic PairsPrinciple 2 : Yin and Yang are inter-penetrating into eachother, and there is no clear boundary between the two(inter-penetration) . Similar patterns exist at differentlevels of objects and properties, but such periodicalrepetition is never exactly the same . (recurrence)The inter-penetration nature of YiniYang pair comes

from Chinese people's belief of the creation of the world(Figure 2). They believed that the very beginning of theworld was pure chaos, firstly splitting into Yin and Yang,then each of them further divided into one relatively Yin

Eight-Hexagrams

t

E :Yin

1 WesternApproach

*The wholepicture can be fit recursively into any ofthe two small circles periods.

Figure 2 : T'ai-Chi Svmbol

QR99 Loch Awe, Scotland

Table 3 : Comparison of Eastern versus Western Approaches

and one relatively Yang part, further splitting willproduce Eight-Hexagram, and so on. The process went onuntil finally it produced the great variety in the world .

It's interesting to note that one can always find some"Yang" characteristic in "Yin", and vice versa, just as theevidence of opposite gender characteristic on one other . Iflooking from a broad view, we can find "Yin" aspects inWestern Science and "Yang" aspects of Eastern Science(Figure 3) ; if looking into the Western Science, we canalso recognize subjects such as mathematics and physicsare "Yang" while social science and behavior science are"Yin" . However, a more detailed look will show thatchaos theory in physics is an "Yin" element, while it's acommon practice for social science and other "soft"science to borrow principles from physics and borrowtools from mathematics .

OYin OYang

Figure 3 . Nested View: Eastern versus Western Science

Dynamic Nature of Yin/Yang Dichotomic PairsPrinciple 3 : Everything keeps on changing under theinteraction and transformation between the oppositeforces of Yin and Yang (mobility) . The balance point mustbe somewhere in the middle and the two extremes willnever be reached, since reversal will take place wheneverone extreme is about to be reached (reversibility) .This dynamic nature of Yin-Yang dichotomic pairs can

be best illustrated by the development of modern scienceitself. There are roughly three stages in the developmentof modern science, which show an overall recursivepattern .

130

3

Methodolor_4y Yin-Yang (Eastern) Scientific Research (Western)Ob jective Emphasize the relationship between objects Em thasize the objects themselves .Direction Start from understanding the intrinsic law of Start from collecting data from real life

the world and objects as a whole, and then phenomena, try to reduce the data, andtry to apply the law to real life problems . understand the world through laws derived(deductive) from data reduction . (inductive)

Method Holistic ReductionistGoal Be in harmony with the world Conrluer the worldTool Symbolic system : T'ai-Chi symbol (Capra Mathematical language,

1975, pp . 107), Eight-Hexagrams, Sixty-four Data, modeling and analysis, etc.Hexa rams(Zhu Xi 1992)

Characteristics Fuzzy, abstract, holistic, Precise, concrete, fragmentary, more detailed,More conceptual, qualitative joluantitative

Western Dualism Eastern Science '4 great inventionsScience (Kant 1724 (Yin-Yang, '(Gunpowder,(Newtonian) 1804, Hegel ' Five Element Compass, Paper,

t770-1831) ' System) Printing)

During the first stage (before the 15th century),Western natural science was dominated by the philosophyof Aristotle (384322 BC), who took an organic view ofthe world, tried to understand rather than predict orcontrol it . This approach is closer to the Eastern way of"Yin", but was evolved around the concept of "God"rather than the nature itself.The second and most influential stage was from 16th to

18th century . During this period of time, a whole newscientific paradigm was set up and subsequently led toachievements in almost all disciplines . The world thenwas viewed as a Cartesian or Newtonian machine, whichalthough extremely complex, could be broken down intoits components, and be analyzed through each component,be exploited, controlled and destroyed respectively (Capra1988) . We can see that in this stage, the scientificapproach moved towards the "Yang" side, departing fromthe first stage of the relatively "Yin" side of view .The achievement that humankind had made by

adopting the mechanistic worldview was tremendous.Nevertheless, the methodology does not match today'sproblems, which increasingly reveal new levels ofcomplexity of interrelated processes and contingenciesacross multi-culture domains (Skyttner 1998) . The worldkeeps on changing and new methodologies and paradigmsare always needed when new phenomena are debated(mobility) .At the beginning of the third stage, from the end of

19th century to the early 20th century, a significantreversal took place with the emergence of Einstein's(1879-1955) special and general theories of relativity andquantum mechanics by Bohr (1885-1962), Heisenberg(1901-1976), and Schrodinger (1887-1961) . Importantphysical quantities, such as space, time and mass, whichhad previously been considered as absolute concepts allproved now to be merely relative . After discovering thatthe physical relationships at the subatomic level are non-deterministic, physics has gradually moved towards anon-deterministic worldview (Hunt 1994) . Likewise, thediscovery in quantum mechanics that the observer of ascientific experiment will inevitably influence itsoutcome, that is, every observation and scientificstatement is relative, is slowly having a great impact inother disciplines. Contemporary science puts increasinglymore emphasis on relative rather than absolute conceptsand truth, systemic approaches rather than purereductionism (Daellenbach 1995, Ciborra 1998, Skyttner1998), qualitative versus quantitative descriptions (Hayes1985), nonlinear rather than pure linear thinking (Mainzer1997), all of which are consistent with the Yin-Yangphilosophy .

Here, both the dynamic nature and the recursive patternare evident in the development of western modern scienceitself.

QR99 Loch Awe, Scotland

Quantitative Reasoning

Call for Integrative FrameworkBy relating Yin and Yang with different functionsprovided by the left and the right brain hemisphere, Sodan(1998) spot the long underestimation of right-brainmethods (Yin) in Western Science. He reasons that due tothe growing complexity and diversity of problems and theinability to solve them using one-sided approaches, thereis a trend towards the integration and harmoniousbalancing of fully developed poles in Computer Science :the combination of numerical and non-numerical (i .e .qualitative and quantitative) applications ; of theory andpractice, of shared- and distributed-memory architectures,etc . And therefore, Sodan calls for more research into theinherent potential there.

Similarly, Minsky (1991) calls for new research effortsto develop integrative Artificial Intelligence frameworksand methodologies to overcome the currentlypredominating dichotomy of symbolic reasoning andconnectionist methods . He argues that the solution to theinflexibility of both types of AI system lies somewherebetween these two extremes, rather than the furtherseeking in either direction as we used to do . Minsky'sidea is surprisingly close to our Yin-Yang theory eventhough he is not arguing in terms of Eastern philosophy ofscience at all . He develops his argument mainly along thetraditional western approach of Al research . We identify,in Table 4, a set of dichotomy pairs that are predominantin current AI research .

YinConnectionist

Analogical ReasoningApproximate Reasoning

Common SenseBreadthHeuristic

Fuzzy/ApproximateMulti-PerspectiveGlobal SearchBottom-Up -

YangSymbolic SystemNumeric ReasoningLogical ReasoningDomain Specific

DepthTheorem

Precise/AccuracySingle-PerspectiveLocal Optimization

Top-DownTable 4 : Yin-Yang Pairs in AI Research

Such kind of consistency between Marvin Minsky'sproposed framework with the Yin/Yang theory can't beeasily explained away by mere coincidence. The drivingforce behind that, just as we've mentioned before, is thecomplex nature of the problems that we are facing . Theaim of AI is to mimic intelligent behavior to the greatestextent, while human intelligence intrinsically requires theintegrative efforts from both the left and the right brainhemisphere, both numerical and symbolical processing,and both qualitative and quantitative representation .

Specifically, we argue that Qualitative Reasoning, orcommonsense reasoning, could be developed as an

4

integrative modeling framework balancing the Yin andYang aspects. In the following sections, we will analyzeQR modeling methods by applying Yin/Yang theory, andpropose the new framework correspondingly .

Trade off Issues in Model Building

Quantitative versus Qualitative Methods . Having theadvantage of producing precise results, at the cost, ofcourse, of committing to certain modeling assumptions,quantitative approaches are widely used in almost allnatural science such as physics and mathematics, but alsoin the social science, management and economics .Traditional quantitative methods frequently suffer fromthe lack of confidence in the appropriateness of theunderlying model (Freedman 1992, Lang et . al . 1995),since information is hardly complete, relationships areoften vague, and precise modeling of the real worldsituations is almost impossible .

Fortunately, however, we do not necessarily needprecise answers . A qualitative prediction can be goodenough in lots of cases (Hinkkanen et . al . 1995, Fishwick1989) . Therefore, as our information of the world isincomplete and often qualitative, we may as well settlewith qualitative results, and thus depend on fewerassumptions and wider applicability (Kuipers 1993) .

From a Yin-Yang point of view, quantitative methodsare "Yang" while qualitative methods are "Yin" (recallTable 2). Therefore, they are two complementary methodsof tackling the same problem, they are not mutuallyexclusive (as the general impression might be), but rathercan be considered to be the two endpoints of onecontinuum . Furthermore, there is no sharp dividing linebetween qualitative and quantitative methods and we arealways somewhere between the middle of the two . Forexample, Kuipers and Berleant (1990) developed a hybridreasoning system, QSIM/Q2, that combines purelyqualitative reasoning with interval-based numericalreasoning .

Information Cost versus Model Precision . The realnumber line can be viewed from either a qualitative orquantitative perspective . Using a qualitative scale, it mayrepresent the qualitative distinctions of negative, zero andpositive . As a quantitative scale, it represents the orderedset of the real numbers.

Alternating back-and-forth between qualitative andquantitative representation is also common in behavioralresearch, where the Likert scale is often used to measurequalitative responses from subjects . For example, in aquestionnaire, a 5-point Likert scale would usually use 1for representing "strongly disagree", 2 for "disagree", 3for "neutral", 4 for "agree" and 5 for "strongly agree" .The numerical values will then typically be used in somestatistic analysis to come up with some numerical results .

QR99 Loch Awe, Scotland

Finally, these results will be translated back andinterpreted as a qualitative answer.

However, the back-forth process is not so easy when itcomes to model building where information cost has to betraded off with model precision . Although it might looksimple and obvious, the choice of a cut-off line is by nomeans an easy task in the sense that it depends on thelevel of precision, accuracy and reliability, as well as thedifficulty and complexity of modeling scenario. Whetherwe should further validated and quantify the model orstop building and start using it is always a perplexingquestion to researchers . The optimal choice depends onthe problem context and, again, lies somewhere inbetween . Some economists have studied the tradeoffbetween the model building cost of acquiring (moredetailed) information and the extra benefit resulting froma more precisely specified model (Balakrishnan andWhinston 1991) .

Qualitative SimulationQualitative Reasoning (QR), or Qualitative Physics,

basically incorporates two central tasks : to identify thestructure of a system (modeling), and to derive and toexplain its dynamic behavior (Werthner 1994) . Inquantitative modeling, a real number is used to describean attribute of a real physical object and explicit functionsare used to describe the relationship between variables .However, complete quantitative knowledge containsinformation that is typically not available, while thehuman cognitive capacity may be too limited to evenascertain as little as a single number (Forbus 1988,Kuipers 1994) . The emergence of qualitative reasoning asa new modeling tool coincides with other new methodslike probabilistic reasoning, fuzzy modeling, chaos theoryor systems thinking, that emphasize uncertainty,dynamics, and inter-connectedness .

There are mainly two types of qualitative reasoningsystems : one is Qualitative Simulation (QSIM) proposedby Kuipers (1986), the other is Qualitative ProcessTheory (QPT) proposed by Forbus (1984). The process-centered approach by Forbus describes changes in thephysical world in terms of dynamic and interactiveprocesses, which is quite similar to the mobility principleexpressed by Yin-Yang theory . In QSIM, however, thequalitative behavior of the system variables is describedas bi-directional relationships called QualitativeDifferential Equations (QDE) . The system behavior willbe predicted from a qualitative problem description byruling out impossible combinations .

Landmarks. In qualitative reasoning, numbers arerepresented in usually three ways: signs, inequalities, andorder of magnitude (Forbus 1988) . Basically, however,they are different ways of using qualitative landmarks todescribe variables . First, when we use signs to represent anumber, there is a landmark of zero by default . Second,

5

the use of inequalities is based on the introduction ofexogenous or endogenous new landmark values . Forexample, temperature of the water (Tw) can be expressed

Tfreeze--)0, Ts,---r Tt.,,,,

as inequalities (Forbus 1988) representing a partiallyordered sets of qualitative values :Where Tk, is bigger than Tf,,,, and less than both T stover

and Tboii. Thirdly, landmarks are more explicitly usedwhen describing the orders of magnitude . Forbus andKuipers define a quantity space as a partially ordered setof landmark values, where a quantity is described in termsof its ordinal relations with the landmarks (Kuipers 1986) .This representation of numbers corresponds very well

to the Yin-Yang splitting idea. As we mentioned before, ifwe view the whole set of numbers as an infinite line, thenone end is Yin (- ), the other end is Yang (+ ). Whenthe line is split into two in the middle, two regions arecreated, symbolized as "+" and `=" . With the introductionof more landmarks, the line is further split, and thedescription of numbers is more and more refined, whichmeans we are moving gradually from a qualitativetowards a quantitative knowledge representation . Whenthe width of the intervals between landmark values issmall enough, we are approaching a more quantitativerepresentation . We can't say exactly when this changehappens, because there is no clear cutting point betweenYin and Yang . What we do know is that it must be acontinuous process, where back and forth happens all thetime . This "split" idea is also very similar to the Yin-Yang theory of how varieties of this world are created bythe ever-lasting splitting behavior of Yin and Yang .Furthermore, QSIM allows new landmarks to bediscovered during the qualitative simulation, and then usethem to define new qualitative distinctions, which in turncreates new behaviors. However, too many distinctions orlandmarks lead to prolific behavior trees and intractablebranching (Kuipers 1987), which means an overemphasisof Yin . Just as we know from Yin-Yang theory, thatsplitting of Yin and Yang will produce new identities .

Here, we can also identify a trend in the efforts madeby QR researchers to add quantitative features to QSIMso as to increase the quality and precision of modeloutputs . Kuipers and Berleant (1990) improved theoriginal version of QSIM by introducing numerical rangesfor landmarks to describe variables ; Raiman (1988)introduced order of magnitude reasoning ; and Berleant(1990) made another effort by including probabilitydistributions in QSIM to derive probabilities for theparticular qualitative behaviors. These are all niceattempts to push QSIM from its purely qualitative (Yin)Position to a more balanced middle point in between . Andthe inclusion of numerical information, when available, inQSIM clearly improves its accuracy in predicting systembehavior.

QR99 Loch Awe, Scotland

Qualitative Differential Equations (QDE). QualitativeSimulation (QSIM) is the prediction of the possiblebehaviors consistent with incomplete knowledge of thestructure ofphysical system (Kuipers 1993 p.133) . Whileincompletely known values may be describedqualitatively in terms of their relations with a discrete setof landmark values, incompletely known functionalrelations may be described qualitatively as monotonicallyincreasing or decreasing, passing through certaincorresponding landmark values.A Qualitative Differential Equation (QDE) is an

abstraction made from Ordinary Differential Equations(ODE), this abstraction from numerical values tosymbolic names depends on the fact that the familiararithmetic operations that we perform on numbers havecorresponding algebraic operations on symbolic namesand expressions (Kuipers 1994) . It's composed ofvariables, quantity space, constraints and transitions . Asimple qualitative constraint can be expressed as : Y=M+ (X), which means variable Y monotonically increasesin variable X (and vice versa) . For example, we know thatpressure at the bottom of a container will increase will theamount of water it contains . However, we may not knowthe exact relationship between the two, therefore, we canexpress it as :

Pressure A =11?' (amount A)This information is enough for a QSIM simulation . The

whole mechanism can be illustrated by Figure 4 . Forexample, we may obtain an approximate function or anestimation of the relationship between the pressure andamount from observations or by assumption, which mightbe Y= aX2 + b, and then perform ordinary calculation toget a precise number of pressure at the bottom of thecontainer when a certain amount of water is poured intothe container. Alternatively, it would be viewed as part ofthe system and left as a relatively implicit QDErelationship, and then we get a QSIM solution fromqualitative reasoning . The qualitative and quantitativeresult should be consistent with each other, sincequalitative reasoning is only an abstraction of the system,which should be consistent with any possible-valuedquantitative descriptions . Just as landmarks can be refinedby the introduction of numerical ranges, those monotonicfunctions can be limited to certain ranges by boundingfunctions as indicated in Figure 4 (Kuipers and Berleant1990) .

Abstraction

Yin El :YangFigure 4 . Qualitative versus Quantitative Reasoning

133

6

Y= aX2 + b Parameter ` Y= M-(X)

Parametmestmat ranges ,a = f(ai, . . .,ao) a C (St~w.w`ga~b=f(bl,. . . .bm) h e (b,_bh,~ .

Ambiguity Problem of QR. There is always sometradeoff when choosing between qualitative andquantitative methods. While qualitative reasoning is morepowerful in the sense that it needs much less arbitraryassumption about the system, the result of QR does havethe problem of ambiguity . Sometimes, the qualitativesolution (the behavior tree in QSIM) may be tooambiguous (too many branches) for a sensible andcomprehensible result (Kuipers and Chiu 1987) .However, consistent with Yin-Yang theory, where there isno exactness but inherent ambiguity, seeking uniquelydetermined problem solutions is not necessarily the mostfavorable modeling approach. Recalling Minsky (1991),we should always seek for something in between .

This is exactly what we are doing in QR, where it'sclear that model building has to neglect some aspects andattributes of reality, and that simplification andabstraction are inherent features of mapping the "infinityof reality" to a finite description . Numerical solutionsrequire exact knowledge, such as data, structure andtechniques, which very often is not available . At the sametime, numerical simulations provide precise answers toprecise questions and assumptions, but very often weneed an alternative or want to have a solution for an entireclass of problems . QR, then, suits this need very well inthat qualitative knowledge can be seen as a layer on top ofthe quantitative one and may even guide the applicationof quantitative knowledge (Werthner 1994) . In fact,qualitative physics can be viewed as the attempt tosystematically relate formal mathematical methods andcommonsense reasoning, and has been mainly evaluatedby matching its results with classical methods ofmathematics and physics (Huberman and Struss 1992) .When we move from quantitative (Yang) to qualitative

(Yin) approaches, using qualitative methods, the problemof ambiguity inevitably comes . Yet the correct answerwill be covered by the set of possible answers,independent of the level of ambiguity . In that sense,ambiguous solutions are not incorrect and may very wellbe considered sound . According to the reversibilityprinciple of Yin-Yang theory, when there is too muchambiguity, we should seek ways to reduce it (Kuipers andChiu 1987) . In QSIM, for example, a set of additionalconstraints may be introduced in order to reduce thesolution space and the number of spurious behaviors .Once more, the success attempts will always seek balancebetween two extremes, corresponding to the rightcombination of Yin and Yang, rather than leaning towardseither of the two.

Discussions and LimitationsFrom our previous discussions, we can see theapplicability of Yin-Yang theory to scientific researchmethodologies, the power of which comes from capturing

QR99 Loch Awe, Scotland

the very nature of the world and the mechanism throughwhich the world operates. Properly applied, it should beable to provide some guideline to the modern scientificresearch. Just as Hunt (1994) put: Philosophy is themother of all areas of inquiry (p.223) . Researchers arecalling for new paradigms that can help us understand aswell as analyze new phenomena (Prahalad and Hamel1994) . Various attempts have been made so far incombining qualitative and quantitative approaches, inapplying chaos theory to various domains, in systemthinking, etc . All these new scientific trends represent amove away from the 400-year-old Newtonian world view,resurrecting the long-forgotten Eastern Yin-Yangapproach, although most probably unintentionally .We are anticipating the merging of Western and

Eastern philosophical approaches with a positive impacton scientific research . It wouldn't be a short-term task,however, given the fact that main paradigm shifts mayrequire a time of centuries rather than decades (Skyttner1998) .On the one hand, we already have it in Eastern

philosophy, embed in a whole set of theory developedaround the concept of Yin-Yang ; on the other hand, evenif we do have the overarching terminology or commonlanguage, it remains a challenging task to put it intooperation . We have witnessed some movements, but theyare still preliminary efforts . Progress can be expected if anew paradigm based on a successful combination ofEastern and Western approaches can be developed .However, we know from our Yin-Yang theory that thisprocess can never reach its ultimate end, oscillationbetween the two must be expected, therefore all that wecan do is trying to be as close to the perfect combinationas possible.

ReferenceAckoff, R. L . 1962 Scientific Methods: OptimizingApplied Research Decisions, esp . Chapterl : The Natureof Science and Methodology : 1-29 . New York : JohnWiley & Sons.

Balakrishnan, A.B . ; Whinston 1991 . Informationa Issuesin Model Specification . Information Sytems Research 2(4) : 263-286.

Berleant, D . 1990 . Probabilities of Qualitative Behaviorsfrom Probability Distributions on Inputs . TechnicalReport, AI90-136, Artificial Intelligence Laboratory,Department of Computer Sciences, University of Texas atAustin.

Capra, F. 1975 . The Tao ofPhysics. Third Edition (1991) .Boston : Shambhala .

Capra, F . 1988 The Turning Point. Science, Society, andthe Rising Culture, esp. Chapter 2 : The NewtonianWorld-Machine : 53-74, New York: Bantam Books .

134

7

Ciborra, C. U . 1998 . Crisis and Foundations : an Inquiryinto the Nature and Limits of Models and Methods in theInformation Systems Discipline . Journal ofStrategicInformation System 7 : 5-16 .

Daellenbach, H.G . 1995 . Systems and Decision Making :A Management Science Approach, esp . Chapter 2 :Systems Thinking : 11-20 . John Wiley & Sons. Chichester.West Sussex . UK.

Fishwick, P . A . 1989. Qualitative Methodology inSimulation Model Engineering. Simulation 52 (3) : 95-101 .

Forbus, K . D . 1984. Qualitative Process Theory . ArtificialIntelligence 24 : 85-168 .

Forbus, K. D . 1988 . Qualitative Physics : Past, Present,and Future. Exploring Artificial Intelligence. eds . HowardShrobe : 239-296 . Morgan Kaufmann Publishers .

Freedman, D. H . 1992 . Is Management Still a Science?Harvard Business Review. November-December: 26-38 .

Hayes, P.J . 1985 . The Second Nafve Physics Manifesto,J.R. Hobbs and R . Moore, eds. Formal Theories oftheCommonsense World. Ablex . Norwood. NJ . 1-36 .

Hinkkanen, A. ; K.R . Lang, A.B . Whinston, 1995 On theUsage of Qualitative Reasoning as Approach towardsEnterprise Modeling . Annals of Operations Research .55 :101-137 .

Huberman, B.A . and Peter S . 1992 . Chaos, QualitativeReasoning, and the Predictability Problem . Faltings, B .and Struss P . eds. Recent Advances in QualitativePhysics. MIT Press . Cambridge . Massachusetts . 119-136.

Hunt, S . D. 1994. On the Rhetoric of QualitativeMethods. Journal ofManagement Inquiry 3(3) .September: 221-234.

Kalagnanam, J . ; Simon H . A . ; Lwasaki, Y. 1991 . TheMathematical Bases for Qualitative Reasoning . IEEEExpert. 11-19.

Kuipers, B . J . 1986 . Qualitative Simulation . ArtificialIntelligence 29:289-388 .

Kuipers, B . J . and Chiu C . 1987 . Taming IntractableBranching in Qualitative Simulation . ProceedingsIJCAI : .1079-1085 .

Kuipers, B . J . and Berleant, D . 1990. A SmoothIntegration of Incomplete Quantitative Knowledge into

QR99 Loch Awe, Scotland

Qualitative Simulation, Technical Report, AI90-122,Artificial Intelligence Laboratory, Department ofComputer Sciences, University of Texas at Austin .

Kuipers, B . J . 1993 . Qualitative Simulation : Then andNow. Artificial Intelligence 59 : 133-140 .

Kuipers, B.J . 1994 Qualitative Reasoning : Modeling andSimulation with Incomplete Knowledge. MIT Press .Cambridge. Massachusetts . US .

Lang, K. R . ; James C . M ; and Andrew B . W. 1995 .Computational Systems for Qualitative Economics.Computational Economics 8 : 1-26 .

Lu, C. H . 1990 . Five Element System in ChineseMedicine. First Edition . Xue Yuan Publisher . Beijing.

Mainzer, K. 1991 . Thinking in Complexity. esp . Chapter1 : Introduction: From Linear to Nonlinear Thinking: 1-13 .Springer. Berlin.

Minsky, M. 1991 . Logical versus Analogical or Symbolicversus Connectionist or Neat versus Scruffy . AI Magazine2(65) : 34-51

Prahalad, C. K . and Hamel, G. 1994 . Strategy as a Fieldof Study : Why Search for a New Paradigm? StrategicManagement Journal 15 : 5-16 .

Raiman, O. 1988 . Order of Magnitude Reasoning .Proceeding ofAAAI-88: 100-104.

Sacks, E. 1987 . Piecewise Linear Reasoning . ProceedingsofAAAI-87. 655-659 .

Skyttner, L . 1998. The Future of Systems Thinking.Systemic Practice and Action Research 11 (2) : 193-205 .

Sodan, A.C . 1998 . Yin and Yang in Computer Science.Communications of the ACM41(4): 103-111 .

Werthner, H . 1994 . Qualitative Reasoning : an Approachto Modeling and the Generation ofBehavior. Springer-Verlag, Wien & New York .

Xu, D . Y . 1995 . Zhou Yi and Modern Science. FirstEdition . Guang Dong Educational Publisher . GuangDong .

Yang, X. P. 1993 . Yin-Yang - Chi and Variables. FirstEdition . Science Publisher . Beijing .

Zhu, X 1992. The original meaning of I Ching . Firstedition . Peking University. Beijing.

135

8