Qualitative Reasoning beyond the Physics Domain : TheDensity Dependence Theory of Organizational Ecology*

Jaap Kamps

University of Amsterdam

Abstract: Qualitative reasoning is tradition-ally associated with the domain of physics, al-though the domain of application is, in fact, muchbroader . This paper investigates the applicationof qualitative reasoning beyond the domain ofphysics . It presents a case study of application inthe social sciences : the density dependence the-ory of organizational ecology . It discusses how thedifferent nature of soft science domains will com-plicate the process of model building . Further-more, it shows that the "model building" processcan also help making theoretically important de-cisions, and, as a result, have an impact on theoriginal theory. This will require a shift in focusfrom the "model simulation" process towards the"model building" process.

1 IntroductionDuring the last decades, Qualitative Reasoning(QR) has been an active area of research . Thefield has reached a consensus on the main is-sues. As a consequence of this, the time hascome to think about extending its domain of ap-plication . QR is traditionally associated withthe physics domain. This domain of applicationhas been so dominant that qualitative reason-ing is often called qualitative physics, for exam-ple Forbus (1988) . Extending the domain of QRprompts an interesting question : is the dominantrelation between QR and physics based on onto-logical arguments?

'This research was supported in part by the Dutch Na-tional Science Foundation (grant # 030-50-334) . The au-thors wish to thank Jeroen Bruggeman, Babette Greiner,Michael Masuch, Breannda.n O Nuallain, Liszlo Polos, CisSchut, and two QR-reviewers for helpful hints and sugges-tions. Address correspondence to Jaap Kamps, Centerfor Computer Science in Organization and Management,University of Amsterdam, Oude Turfmarkt 151, 1012 GCAmsterdam, The Netherlands, Tel : +31-20 525 2538, Fax :-+31-20 626 4873, Email : kamps§ccsom .uva.nl .

Gabor Peli

University of Groningen

The application of QR outside the tradi-tional physics domain seems, indeed, possible .Kuipers (1994)1 lists applications in biology(irreversible population change, predator-preyecology), chemistry (chemical engineering), eco-nomics (supply and demand, micro-economics),and medicine (glaucoma, drug metabolism) . Theanswer to our question appears to be negative,there are no ontological reasons to explain whythe majority of QR-research deals with physicsapplications . Does the lack of ontological argu-ments mean that the relation between QR andphysics is purely accidental? Probably not, theremay be other, pragmatical arguments to explainthis relation . A plausible explanation for thehistorical choice to reason about physical sys-tems is the formal, well-understood nature of thephysics domain . This indicates that QR outsidephysics, albeit possible, may still not be the verysame as QR inside physics . The different natureof the domain may require different emphases .This prompts another question: does the appli-cation of QR outside physics require a change inmethodology?It is with these questions in mind that we per-

formed the case study reported in this paper. Theintention of the paper is to investigate the differ-ences between physics and other domains in thecontext of QR. Therefore, a natural choice ofdomain for this case study is a "soft" science do-main . The soft sciences are in many respects theopposite of physics, in beying highly non-formal,less well-understood . We have chosen to build aQR-application in the social sciences .This paper is organized in the following way.

Section 2 gives a short introduction to the frame-work for qualitative reasoning that we used for

'Several other authors have also reported applicationsof QR outside physics .

our research . Section 3 and 4 introduce thedomain of our case study, i .e., the density de-pendence theory of organizational ecology. Sec-tion 5 describes the qualitative density depen-dence model, and summarizes its qualitative be-havior prediction. Section 6 lists the results thatwere obtained during the construction and use ofthe qualitative model. And finally, in section 7we evaluate our case study in retrospect, tryingto answer the questions posed above.

2

Representational Context

The model of this paper is implemented in adomain-independent qualitative reasoning shellcalled GARP (Bredeweg, 1992) . GARP in-corporates many features of the component-centered (de Kleer and Brown, 1984), and theprocess-centered (Forbus, 1984) approaches inQR. Initial conditions are described in case mod-els, the theory itself in model fragments (con-sisting of conditions and givens) . Case modelsand model fragments can be expressed in termsof : entities (like liquid), quantities (like amount),values and derivatives (like {-, 0,+}), and de-pendencies (like (in)equalities, proportionalities,influences, etc.) ; or in terms of other model frag-ments .The behavior of a system during a particular

time period is described by the set of applicablemodel fragments . The behavior over time peri-ods is determined by the application of transitionrules between states of behavior .

3

The Density Dependence TheoryMainstream organizational theories regard or-ganizations as agents that adapt rationallyto changing environments (Thompson, 1967;Mintzberg, 1979). These theories describe or-ganizations from an individual viewpoint. Com-plementarily, a change in environmental resourceconditions affects the whole population of organi-zations . For example, if resource conditions dete-riorate, the total population of organizations willdecline (despite the efforts of individuals to avoidthis fate) . Organizational ecology (Hannan andFreeman, 1989) describes the process by whichorganizational populations grow and decline dueto changing environmental conditions. Organiza-tional ecology abstracts from the rational behav-ior of individuals, populations are solely depen-

dent on the environmental conditions .

The density dependence theory (Hannan andCarroll, 1992) is at the heart of organizationalecology: it describes the dynamics that underliethe growth of an isolated population as a func-tion of the population's density. It serves asa base model for other parts of organizationalecology that investigate the demographic behav-ior of different (sub)populations under changingenvironmental conditions (e.g ., niche strategists,life history strategists) or during reorganization(e.g ., the inertia-fragment (Hannan and Freeman,1989 ; Peli et al ., 1994)) . The density dependencetheory assumes that the founding and mortalityrates of a population are affected by two oppos-ing forces : by the degree of legitimation that thepopulation enjoys and by the intensity of compe-tition between the members of the population.

Legitimation reflects the institutional standingof the population . A high level of legitimationmeans that the organizational population has thestatus of a taken-for-granted solution to givenproblems . Organizations of high legitimation aredesirable partners for other organizations whenmaking exchange relations . Moreover, foundingnew organizations in a highly legitimated popu-lation is also easier . The theory assumes that thefounding rate is directly proportional to the legit-imation of the population, and that the mortalityrate is inversely proportional to it . Legitimationincreases monotonically with density. The bene-ficial effect of growing density is especially impor-tant when there are only a few organizations inthe environment . If organization density is highalready, then the founding of an additional or-ganization does not improve the population's in-stitutional standing significantly. The higher thedensity of a population is, the smaller is the le-gitimating effect of additional organizations .

An intensifying competition between the mem-ber organizations of the population increases themortality. It also decreases the founding rate ofthe population: managers are reluctant to initiatenew organizations if the chance of success is low .The theory assumes that the intensity of competi-tion is directly proportional to the mortality rateand inversely proportional to the founding rate.Since competition is about resources, the inten-sity of competition increases with density. Thedensity dependence theory claims that increasing

density intensifies competition at an increasingrate .The beneficial effects of legitimation prevail at

low densities, while the negative effects of com-petition dominate if density is high. As a result,the demographic rates change with density in anon-monotonic way. The founding rate increasesover the lower density range and decreases abovea certain value. On the other hand, the mortal-ity rate decreases at low densities, and increaseslater. When the two rates becomes equal, thepopulation reaches its equilibrium size : this valueis called the carrying capacity of the given re-source environment .Hannan and Carroll (1992, Chapter 2) give the

following description of the intuitive theory spec-ified above :

Competition The intensity of competition, C,increases with density, N, at an increasingrate . That is, C = cp(N); and cp' > 0 andcp" > 0.

Legitimation The intensity of legitimation, L,increases with density at a decreasing rate .That is, L=v(N);andv'>0andv"<0 .

Founding Rate The founding rate of an orga-nizational population, A, is inversely propor-tional to the intensity of competition withinthe population, and directly proportional tothe legitimation . That is, A oc 1/C and A oc L.

Mortality Rate The mortality rate of an orga-nizational population, a, is directly propor-tional to the intensity of competition withinthe population, and inversely proportional tothe legitimation . That is, y oc C and ti oc1/L.

For environments in with a positive carrying ca-pacity, it is assumed that legitimation exceedscompetition at low densities, that is, Li > Ci fori < N. To avoid negative founding and mortalityrates, the range of the legitimation and compe-tition functions also has to be confined to non-negative numbers. Since legitimation and compe-tition occur in the denominator of the mortalityand the founding rate, respectively, their valuecannot be zero either . That theory assumes thatL>0andC>0.The legitimation and competition functions are

depicted in Figure 1. Competition increases with

N,

Na drrroity

Figure 1 : Legitimation and competition as func-tions of density.

density at an increasing rate, and legitimation in-creases with density at a decreasing rate . In thisfigure, No denotes the initial point, and N,, de-notes the point where legitimation and competi-tion axe equal.

4

Applying The TheoryOur aim is to simulate the growth pattern of pop-ulations, in other words, how the density of apopulation changes over time. Hannan and Free-man (1989) use the Lotka-Volterra definition ofgrowth rate, p, as the difference between found-ing and mortality rates of the population . Thatis, p = A - A. The growth rate can be calcu-lated from legitimation and competition directly :if A = L/C and y = C/L then p = L/C - CIE.'

Figure 2: Growth rate as a function of density.

Figure 2 depicts the growth rate of an organiza-tional population, based on the legitimation andcompetition functions in Figure 1 .

'In fact, founding and mortality rates may differ bya factor . That is, a = a * L/C and /c = b * C/L. Weignore these factors to allow for the direct calculation ofthe growth rates, because the use of a simple model helpsto convey the main point of our argument . Moreover, ifthe factors a and b are given we can rescale the C andL functions to C* and L*, so that A = L*/C* and p =C*/L*. The rescaled C* (L*) still satisfies the criteria ofincreasing at an increasing (decreasing) rate .

We can now investigate the theory's predictionsabout the change of population size . If the en-

Na

To time

Figure 3 : Expected behavior for an empty envi-ronment .

vironment is initially empty (Figure 3), then thedensity dependence theory predicts a sigmoid (orS-shaped) population growth . This growth pat-tern is similar to the well-known logistic curve ofthe Lotka-Volterra model.

5

Qualitative Density DependenceIn section 4 we have established that growth ratep = LIC - CIL. Having only positive legiti-mation and competition values, this means thatp>0ifL>C,p=0 if L= C, and p<0ifC > L . The sign of L - C equals the sign of p.The qualitative model of growth rate therefore isp =Q L - C3

Section 3 also gives constraints on legitimationand competition. Legitimation is increasing withdensity at a decreasing rate, bL/bN > 0 andPL/W < 0. Competition is increasing withdensity at an increasing rate, 6C/bN > 0 andb 2C/bN2 > 0. But instead of derivatives todensity, derivatives to time are needed . If le-gitimation is greater than competition (a grow-ing population) density will increase with time .This means that we can use the derivatives listedabove. This qualitative behavior can be modeledas follows: L ocQ N, bL ocQ 1/N, C ocQ N, andSC ocQ N .If legitimation is smaller than competition (a

declining population) density will decrease withtime. This means that we have to read the top

3To denote the difference between qualitative depen-dencies and their mathematical counterparts, we use "=Q"instead of "=" for equalities, "ocQ" instead of "oc" for pro-portionalities, and "I" for influences .

half of Figure 2 from the right to the left . Inthis part, competition is decreasing with decreas-ing density at an increasing rate, and legitima-tion is decreasing with decreasing density at a de-creasing rate . This means that the second-orderderivatives of L and C change . This qualitativebehavior can be modeled as follows: L ocQ N,bL ocQ N, C ocQ N, and bC ocQ 1/N.If density is increasing, it has a positive effect

on the second order derivative of competition anda negative effect on the second order derivative oflegitimation . If density is decreasing these effectsare reversed . In the equilibrium points (legitima-tion equals competition, i.e ., No and N,,), densityis not changing, making this difference disappear.

Figure 4: Dependencies of qualitative density de-pendence .

Figure 4summarizes the model. Dependencies 1to 3 are included for technical reasons, they allowthe use of higher-order derivatives by modelingthem as normal values . Dependencies 4 and 5ensure that legitimation is increasing with den-sity at a decreasing rate (if legitimation is smallerthan competition, dependency 6 replaces 5) . De-pendencies 7 and 8 ensure that competition isincreasing with density at an increasing rate (iflegitimation is smaller than competition, depen-dency 9 replaces 8) . Dependency 10 calculatesthe growth rate from the legitimation and com-petition values .We have now modeled the causal chain of the

density dependence theory : i) the trade-off be-tween competition and legitimation causes a cer-tain growth rate, ii) the growth rate will affect

N I+ P (1 )L I+ bL (2)

C I+ SC (3)L ocQ+ N (4)

bL ocQ- N (5)(bL ocQ+ N) (6)

C ocQ+ N (7)

SC ocQ+ N (8)

(bC ocQ- N) (9)

p =Q L - C (10)

2

z6LO ac0

BL+ > BC+L + - C + P

N

+

0

2

26L-

ac+SL+ > SC+L + > C + p +

N +

IL- 6C+SL+ > SC+L + > C +

state 1

Spate2

State 3

State 4

states

State 6

11

A

A

r~

Az z

L .CandSL>SC

N-Oand p ~+

al>SCandSL<SC

5L-SC andSL<a0

L>CandSL<aC

results in L>C

results in N - +

results In S L . S C

results in S L < S C

results in L .C

the density of the population, iii) the change indensity, in its turn, will affect competition andlegitimation, iv) etcetera .Using this qualitative density dependence

model, the qualitative reasoning shell GARP canmake behavior predictions of the following casemodels :

Case A: An empty environment (see Fig-ure 5) . In this scenario, N = 0, L = C, andSL > bC. State 1 is (just before) the point To,state 2 corresponds to To, state 3 to the inter-val between To and Tl, state 4 to the point Tl,state 5 to the interval between Tl and T2, andfinally, state 6 to point T2.

Case B: A population in equilibrium (seeFigure 6) . In this scenario, N > 0, L = C, bL =

state

0, and bC = 0. Case B results in a steady state.The density of the population is at its carrying

Figure 6 : Case B: A population in equilibrium.capacity.

Case C: An overcrowed environment

(seeFigure 7) . In this scenario, N > 0, L < C, andbL > 6C. State 1 corresponds to the intervalbefore T3, and state 2 to the point T3 .

Figure 5: Case A: An empty environment.

2

28L- ac+SL+ . SC+

p +

L + > C +

N +

N o

P +

N +

2

26L- 6C+SL+ < S C+

L + > C +

.. . . . . . . . . .. . .. . ................ ..... ... .. . . . . -

r

SLO 3CO

61.0 . SCO

p 0

L + . C +

N +

6LO sCO

SL+ < &C+p 0

L + . C +

N +

- .

N¢

No

6 Results

.. . . . . . . ........ .... . ... .... .. .. . . . . . . . . . . . . . .-

PN +

SL- SC+

SL+ > SC+

L + < C +

state 1

State Z

L<Cand8L>SC

results in L .C

2

2SLO SCO

SL+ > SC+

P 0

L + . C +

LN +

Figure 7: Case C.- An overcrowded environment.

Hannan and Carroll (1992) give a formal mathe-matical model of density dependence, as well asan explicit qualitative description using the pro-portionalities and the signs of the derivatives assummarized in section 3 . The qualitative descrip-tion provides the intuitions underlying the math-ematical description of the theory. For buildingthe qualitative model, we only used the qualita-tive description of the theory . This resulted ina intuitive model. It describes the core elementsof the theory and abstracts from unnecessary de-tail . The model can be used learn the theory andthe theory's predictions. The resulting qualita-tive density dependence model is able to derivethe behavior predicted by the theory. The qual-itative model is more general than the paramet-rical model (and the resulting quantitative sim-ulations) . A quantitative, parametrical modelmakes, out of necessity, various non-trivial as-sumptions about parameters, functions, etcetera.During the modeling process we had to make

several decisions of theoretical importance . Thesedecisions reveal implicit assumptions underlyingthe theory. Making these assumptions explicit isan important contribution to the original theory.Apart from identifying hidden assumptions un-derlying the theory, the qualitative simulator was

also able to predict unidentified consequences ofthe theory. We will discuss some of these implicitassumptions and consequences in detail .First, the theory gives no information about

the derivatives of legitimation and competitionat zero density. Therefore, it is possible that thederivative of competition is initially higher thanthe derivative of legitimation, i.e ., bCo > bLo(as depicted in Figure 8) . That is, the deriva-

Iogiimation

rrpetition growth rate

N,

density

Ne

\ density

Figure 8 : Monotonically growing population .

tive of growth rate is initially negative, resultingin a monotonic population growth. This is inconflict with the theory's claim that the demo-graphic rates are non-monotonic. A constraint isneeded on the initial derivatives of competitionand legitimation : at zero density, the derivativeof legitimation is greater than the derivative ofcompetition (bLo > bCo) .Second, in state 3 of case A the simulator pre-

dicts a state transition from unequal derivativesof legitimation and competition to equal deriva-tives. Although this transition is likely to occur,it is not guaranteed to take place. In state 3,L > C, bL > 6C, b2 L < 0, and b2C > 0. Thereis no guarantee that bL will become equal to bC.If legitimation and competition behave as in Fig-ure 9, the population will stay in state 3, that is,

Figure 9: Forever expanding population.

it grows exponentially into infinity. This is clearlyunintended : real-world's resources are always fi-

nite . This case can be avoided by assuming thatcompetition exceeds legitimation after a certaindensity value, that is, Ci > Li for i > N (re-call that legitimation exceeds competition at lowdensities) .4Third, the decline of overcrowded populations is

also captured by the density dependence theory. 5If there are more organizations around than thecarrying capacity of the environment, for instancedue to migration, the density falls until the pop-ulation reaches the carrying capacity (see Fig-ure 10) . The theory claims that the density de-

denafty

Nm

N,ertw

Figure 10 : Expected behavior for an overcrowdedenvironment.

pendence of organizational populations is non-monotonic. This is, indeed, the case for increas-ing populations . The decrease of populationsmanifests, in contrast, a monotonic pattern .

7 DiscussionAs discussed in the previous sections, the den-sity dependence theory of organizational ecologywas successfully modeled as a QR-application .In accordance with existing research, our casestudy did not reveal any ontological argumentsthat would prevent the application of QR outsidephysics .A full-fetched discussion of the metaphysics ofQR is outside the scope of this paper. This dis-cussion should focus on the level of abstraction.Physics has reached a high level of abstractionusing terms such as energy or gravity as abstrac-tions of underlying forces . These terms have anadvanced nature (anyone who tried to explain to

'A different remedy, namely to impose an upper-boundon legitimation, is suggested in Peli (1993) .

'This additional case model was found by hand, al-though it could have been discovered using a total-envisionment of states and transitions .

a child what gravity is will have noticed this) .The non-physics domain of this paper and thoseof Kuipers (1994) have also reached a level ofabstraction that is sufficient for building QR_applications .Although feasible, the application of QR in a

soft science domain is somewhat different fromapplying QR in physics . This difference seemsto emerge from the different natures of both do-mains . There is one important difference be-tween the domain of physics and a domain inthe soft sciences . Not surprisingly, soft sciencedomains are less well-understood, less formal-ized . In short, soft sciences lack the deep under-standing of domain knowledge that characterizesphysics . This is a subtle difference, but it hasimportant methodological consequences .6

7.1

Finding the right model for the job

A first consequence is that building models onless well-understood, less formal domains will re-quire more effort, and therefore will be more timeconsuming. Although the value of the "modelsimulation" process (Forbus, 1988) remains, the"model building" process must obtain a moreprominent status .There is another, deeper, consequence . In

physics, terms such as liquid flow have a clearlyestablished meaning (Hayes, 1985) . In the softsciences, the nomenclature is less developed ;there is hardly any consensus . Terms like le-gitimation vary in their precise meaning amongdifferent theories . For example, the term le-gitimation denotes, in the density dependencetheory, the taken-for-grantedness of an organiza-tional population. On many occasions, the pre-cise nature of a variable is only defined by thebehavior it manifests in the context of a theory,and not by its label . As a consequence, the con-structed domain models will not be very generic,they will only be reusable to a very limited ex-tent.In the traditional case (Falkenhainer and For-

6In the following, we will exaggerate this differencein understanding of the domains in order to make ourarguments more clear . In reality, insufficient knowledgeabout the domain can play a role in all domains, includingphysics (as one reviewer put it : "Modeling in the physi-cal sciences and in engineering is still very much an art") .Thus, insights in the way to handle insufficient domainknowledge are useful for QR in general .

bus, 1991), the use of a particular term, say liquidflow, induces the use of a particular model frag-ment specifying the behavior related to this term.But when terminology has no exact meaning thisprocess is reversed : a needed model fragment de-termines the use of a certain term. The predic-tion of certain desired behavior, e.g ., a sigmoiddensity function in the density dependence the-ory, requires the opposing force of two underlyingcauses . After constructing the model fragmentswith unlabeled variables, we start to look for soci-ological meaningful names, for example the termslegitimation and competition, for the two under-lying causes .Summarizing, the application of QR in soft sci-

ence domains will require more effort in the modelbuilding process . Moreover, the constructedmodel fragments will only be reusable to a limitedextent . Thus, it is less likely that the modelingprocess can be facilitated by existing libraries ofgeneric model fragments .

7 .2

Finding the right job for the modelThe same fact that causes the model building pro-cess to be more troublesome, also makes it moreworthwhile . Let us analyze what is disturbingthe modeling process. Is it the "incompetence"of the model builder? Although the bounded ra-tionality of a human model builder is certainly animportant factor that tampers with the modelingprocess, there is no reason why the same modelbuilder should be less competent when modelinga soft science theory . Is it the "incompetence"of the theory? We think so : during the model-ing process many decisions have to be made, thathave an impact on the original theory.The theory can be ambiguous and allow for

various interpretations . If these ambiguities aresolved in the qualitative model, this solution cor-responds also to an improvement of the originaltheory (see section 6 for examples) .' The ex-plication of the underlying structure of a theorywill provide new theoretical insights . The modelcan reveal underlying assumptions, and therebyshed light on the theory's domain of application .Furthermore, the simulator can identify unfore-seen (and even counterintuitive) consequences ofa theory, and thereby clarify the theory's predic-

7Note that handling incomplete knowledge is one of thestrong points of QR.

tive and explanatory power. In short, the originaltheory will evolve in parallel with its qualitativemodel during the modeling process.$Suppose we attempt to build the qualitative

model of a premature, possibly imperfect the-ory. Instead of a straightforward translation, themodel building will require decisions of theoret-ical importance. These decisions can be facili-tated by simulation runs : various alternatives can

Obe implemented and evaluated for their impacton the behavior prediction . The predicted be-havior may not be in accordance with intuitions,logic, or empirical knowledge. These discrepan-cies will guide the model builder in the revisionof the qualitative model (or of the expectations).9Moreover, these revisions will also apply to theoriginal theory. In this way, the tedious "debug-ging" steps in traditional QR acquire a new char-acter. They become experiments at the frontier ofa science: every successful and every unsuccessfulrevision of the model may extend our knowledgeabout the theory.

'Contemporary philosophy of science argues that the-ory development follows a cyclic pattern (Kuhn, 1962 ;Lakatos, 1976 ; Balzer et al., 1987) . After the initial for-mation of a theory, it is repeatedly revised to account foranomalous observations (and may, in the end, be aban-doned if the revision would require too radical changes,resulting in a paradigm shift) . QR can play an importantrole in this diachronic structure of a theory, it allows us torecreate the theory-evolution process at a miniature scale .

'Several machine learning tools to support the evolu-tionary model building process (Falkenhainer and Raia-money, 1988), and the diagnose/repair step (Bredeweg andSchut, 1993) have been reported .

References

Balzer, W., Moulines, C . U ., and Sneed, J . D.(1987) . An Architectonic for Science: TheStructuralist Program, volume 186 of SyntheseLibrary . D. Reidel Publishing Company, Dor-drecht .

Bredeweg, B . (1992) . Expertise in QualitativePrediction of Behaviour. PhD thesis, Univer-sity of Amsterdam .

Bredeweg, B . and Schut, C. (1993). Re-ducing ambiguity by learning assembly be-haviour . In Proceedings of the 13th International Joint Conference on Artificial Intelli-gence '93, pages 980-985 . Chambery, France,August 1993.

de Kleer, J . and Brown, J . S . (1984) . A quali-tative physics based on confluences . ArtificialIntelligence, 24:7-83.

Falkenhainer, B . and Forbus, K . D . (1991) . Com-positional modeling: finding the right modelfor the job . Artificial Intelligence, 51 :95-143 .

Falkenhainer, B . and Rajamoney, S . (1988). Theinterdependencies of theory formation, revi-sion, and experimentation . In Proceedings ofthe 5th International Conference on MachineLearning, pages 353-366 . University of Michi-gan, Ann Arbor MI.

Forbus, K . D . (1984) . Qualitative process theory .Artificial Intelligence, 24:85-168 .

Forbus, K. D. (1988) . Qualitative physics : Past,present and future . In Shrobe, H. E ., editor,Exploring Artificial Intelligence : Survey Talksfrom the National Conference on Artificial In-telligence, chapter 7, pages 239-298 . Morgan-Kaufman CA.

Hannan, M. T . and Carroll, G . R. (1992) . Dy-namics of Organizational Populations : den-sity, legitimation, and competition . OxfordUniversity Press, New York, Oxford.

Harman, M . T. and Freeman, J . (1989). Orga-nizational Ecology. Harvard University Press,Cambridge MA.

Hayes, P. J . (1985). Naive physics I : Ontologyfor liquids . In Hobbs, J . R. and Moore, R. C .,editors, Formal Theories of the CommonsenseWorld, pages 71-107. Ablex Publishing Corp .Norwood NJ .

Kuhn, T. S . (1962) .

The Structure of Scien-tific Revolutions . University of Chicago Press,Chicago .

Kuipers, B . J . (1994) . Qualitative Reason-ing: Modeling and Simulation with IncompleteKnowledge . MIT Press, Cambridge MA.

Lakatos, I . (1976) . Proofs and Refutations . Thelogic of mathematical discovery. CambridgeUniversity Press, Cambridge, England .

Mintzberg, H. (1979) . The Structuring of Orga-nizations. Prentice-Hall, Englewood Cliffs NJ.

Peli, G. (1993) . A logical formalization of popula-tion dynamics : the density dependence modelof organizational ecology. Technical Report93-106, CCSOM.

Peli, G., Bruggeman, J ., Masuch, M ., and 0 Nu-allain, B. (1994) . A logical approach to formal-izing organizational ecology. American Socio-logical Review, 59(4):571-593 .

Thompson, J. D . (1967) . Organizations in Action.McGraw-Hill, New York.