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PhilosophicalFoundationsofConceptualModelsJohnMylopoulosUniversityofOttawaCentrodeInformática,FUPERecife,November20,2019

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Acknowledgements  This is joint work with Nicola Guarino and Giancarlo

Guizzardi.MyviewsonConceptualModellingsincetheearly1970s were heavily influenced by ideas of Alex Borgida(RutgersU, emeritus) and Hector Levesque (UToronto,emeritus).

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AbstractWereviewandanalyzealternativeanswers to fundamentalquestions for ConceptualModelling, such as: (a)What is aconceptual model? (b) Among models used in ComputerScience,whichareconceptualandwhicharenot?(c)Howareconceptualmodelsdifferent fromothermodelsused in theSciencesandEngineering?OurstudydrawsfromliteratureinPhilosophy,CognitiveScience,Logics,aswellasseveralareaswithin Computer Science, including Databases, SoftwareEngineering (SE), Artificial Intelligence (AI), InformationSystemsEngineering(ISE),amongothers.

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Motivation  ArecentERpaper[Delcambre18]proposes“AReference

Framework for Conceptual Modelling” that attempts toanswerfundamentalquestionsaboutConceptualModelling(CM),suchas:What isand isn’taconceptualmodel (cm)?Whodoesconceptualmodelling?Etc.  Weapplaudtheeffortsofourcolleagues,thisdiscussion

islongoverdue!  For CM to be a respectable research area, it needs to

reachconsensusonwhatcmandconceptualmodellingare,and what are the research questions that need to beaddressed.  Thispresentationdrawson[Guarino19].

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Conceptualmodels  It isabasictenetofCognitiveScienceandPhilosophyof

Mind that cognitive processes create, use and transformmentalrepresentationsoftheworld[SEP05].  These representations can be conceptual (consisting of

concepts), for example thoughts, or non-conceptual, e.g.,sensations (aka tacit knowledge). We call the formerconceptualmentalrepresentations.  Conceptual models are computational models of

conceptualmentalrepresentations,tobeusedforpurposesofunderstanding,communicationandproblemsolving.  Conceptual models are different from other kinds of

modelsused inScienceandEngineering in that theydon’tmodel theworld,butratherourconceptualizationsof theworld.

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Whycomputational?  Conceptual models are computational in that they are

stored in computers and are analyzed or reasoned withthroughcomputationalmeans.Computationality renders conceptual models scalable and

analyzable. Pragmatically speaking, it is inconceivable thatconceptual models would be useful “for purposes ofunderstanding, communication and problem solving” if theywerenotcomputational.  It is no accident that they came aboutwith the advent of

computers.

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Conceptsasatomsofthought  Concepts are the atoms of conceptual mental

representations. They are formed through experience (Locke,Hume), including social interaction, and provide a “lens forlookingattheworld”,or“alanguageofthought”[Fodor75].  There seems to be consensus that concepts come with a

definitional structure, they are associated to other concepts(associationism,see[SEP18])andhaveinstances/referents(seeFregeetal).

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Conceptsandassociations  ConceptshavebeenatopicofstudyinPhilosophysincePlato

and Aristotle; Associationism has been studied at least sincetheempiricists(Locke,Hume).  Together they constitute the philosophical foundations of

ConceptualModelling.  Conceptual modelling languages adopt this perspective:

semantic networks, semantic data models, description logics,OOmodels,businessprocessmodels,…  Others modelling frameworks adopt a logical perspective:

Concepts have a propositional, rather than an associationist,structure.

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OriginsofCMinComputerScience  In AI, Ross Quillian proposed semantic networks as a

modelofthestructureofhumanmemory[Quillian66].  In Programming Languages, Ole-Johan Dahl proposed

Simula,anextensionofALGOL60,forsimulationprogramsthatrequire“worldmodeling”[Dahl68].  InDatabases, Jean-RaymondAbrialproposedasemantic

modelin1974[Abrial74],shortlyfollowedbyPeterChen’sentity-relationshipmodel[Chen76]asadvancesoverlogicaldatamodels,suchasCodd’srelationalmodel.  Doug Ross proposed in the mid-70s the Structured

Analysis and Design Technique (SADT) as a “language forcommunicatingideas”[Ross77].Thetechniquewasusedtospecifyrequirementsforsoftwaresystems.

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Semanticnetworks(1966)

Novelideas  Modelsarebuiltoutofconceptsandassociations  Inheritanceofattributes--default,single  Computationdefinedintermsofspreadingactivation--e.g.,discoveringthemeaningof“horsefood”

horse-->animal-->eat-->foodhorse-->animal-->madeOf-->meat-->food

Animal

Bird-canfly Fish-canswimMammal

Penguin-can’tfly Shark

Human

eats

Feather

has

isa

isa

isa

isa

isa

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Simula(1967)

  Ole-JohanDahlproposeditasanextensionofALGOL60,forsimulationapplications.

  A(simulation)programconsistsofclassesandinstances.  Instances model the simulated domain, classes definecommon features of instances, are organized into subclasshierarchies.

person

heightweightcoors

customer

haircutPeriodhaircutPriceenterQueuepayBillnewC,delC

person

heightweightcoors

barberShop

queuebarbersserveCustomergetPaymentnewBS,delBS

person

heightweightcoors

barber

haircutTimesalarygiveHaircutnewB,DelB

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Entity-RelationshipModel(1975)

Novelideas  Assumes that application consists of entities andrelationships(ontologicalassumptions)

  Shows how a conceptual schema can be mapped onto alogicalone.

  [Abrial’s semantic model was more akin to OO datamodels,butdidofferentitiesandrelationstoo]

Customer M1

Places/PlacedBy

M

MContains/isContained

Book

Order

Customersplaceorders;eachordercontainsmanybooks

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StructuredAnalysisandDesignTechnique(SADT)

NovelIdeasü Modelingthe

operatingenvironmentofasoftwaresystem.

ü  Applicationmodelsorganizedintermsofbox-inside-boxnotation.

BuySupplies

Cultivate

ExtractSeeds

Seed&VegiePrices

Plan&Budget Weather

PlanBudget

Fertilizer

Seeds

Plants

Vegetables

PickProduce Vegetables

GrowVegetables

Money

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HistoryofConceptualModelling  In AI, semantic networks served as foundation for

knowledge representation languages, e.g., KLONE[Brachman78]and[Levesque79],leadingtoDescriptionLogics[Baader03]andOWL,aWWWstandard.  Dahl’s Simula included classes and their instances for

modelling a domain, evolved into Smalltalk at Xerox PARC,andledtoOOModellingandUML.  InDatabases,theExtendedERModelandUMLareusedfor

conceptualschemadesign.  InRequirementsEngineering,SADTwasfollowedbyformal

modelling languages, e.g., [Greenspan82] and Goal-OrientedLanguages,e.g.,KAOS[Dardenne93],i*[Yu97].  NewresearchthreadsonConceptualModellinghavesprang

in Business Process Management (BPM), EnterpriseArchitectures(EAs)andmore.

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Commonthread  The common thread that underlies all these efforts is an

attempttobuildmodelsthatviewadomain“thewaywedo”and are consequently “direct and natural” models[Hammer78],“capturetruesemantics”[Roussopoulos75].  In AI and Knowledge Representation (KR) these models

serve as knowledge bases for artificial agents to conductproblemsolving.  In Databases, SE, BPM, EA they serve as useful design

models for databases, software, business processes,enterprises,etc.  Important difference between KR and other areas of

Conceptual Modelling: KR places great emphasis onreasoning with a conceptual model, whereas other areasfocusonusingtherightontologytobuildtherightmodel.

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Buthowdoweknowanythingaboutourconceptualizations?  From things we say about our conceptual mental

representations.  For example, if you ask a database administrator to

describeforyouthecontentsofherdatabaseandshetellsyou that it’s about students taking courses, havingmarks,etc.,youcancomeupwithanEERschemaforit*,**.______________* But not a relational schema, because that is not aconceptualmodel.**Actually,Databasestextbooksdoteachhowtogofromanatural languagedescriptionofthecontentsofadatabasetoaconceptualschema,e.g.,[Atzeni99].

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ModelsinScienceandEngineering  Theyareusuallymodelsofthespatio-temporalproperties

ofphysicalthings,atleastforPhysicalSciences.  They are objective in that they model the domain, not

someone’sconceptualizationofthedomain.Moreover,theyarenotconceptual inthattheydon’t includeintheirmodeltheconceptstheyuse.  Take a model of a building: Engineers use measuring

instruments to construct a 3D model, but there is norepresentationoftheconcepts‘wall’,window’,etc.  In CM, we may build a cm for a building by asking 10

occupants to describe their conceptualizations of thebuilding.

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ConceptualmodelsinsomeSciencesandEngineering  Conceptualmodelsoffersubjectiveviewsoftheworld.  Some Sciences need such models, including Cognitive

Science, Sociology, Law, Economics/Management Sciences,andComputerScience,tonameafew.  SameforEngineering:MuchofEngineeringhastodowith

the design of artifacts [Simon69]. And conceptual modelshaveproventhemselvesessentialtoolsfordoingdesign.

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Newton’ssecondlaw,conceptuallyandotherwise  ThelawstatesthatF=M*A,whereFstandsfor‘force’,M

for‘mass’andAfor‘acceleration’.  But where are the concepts? Obviously, M and A are

qualitiesofaphysicalobjecto,whileFrepresentsanaction(push) a applied to that object, and the law is relating thestrengthoftheactiontotheobject’sphysicalproperties.  Aconceptualmodelofthis lawwould includeentityclass

PhysObject with attributes mass, velocity andacceleration, action class ApplyForce with object andstrengthattributes.

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Completenessofconceptualmodels  Sinceconceptualmodelsaretobeusedforunderstanding

and communication, they must satisfy two completenessproperties:

ü  Everyinstancemustbeassociatedtorelevantclassesitisaninstanceof(noinstancewithoutitsclasses);

ü  Every quality attribute should be associated to theobject it is an attribute of (no attribute without itsobject).

  Conceptual models are actually used in Physics forpedagogical purposes [MacKay19], but not for definingphysicallaws…

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Conceptsmusthavecoherence  Manyconceptualmodelling languagesmodel conceptsas

unarypredicatesandusetheconnectivesofLogictodefinenewconcepts. Forexample, Imay represent conceptsManandUnmarriedwithpredicatesMandUandthendefinetheconceptB(achelor)asM ∧ U.  Accordingtothisview,¬MandM ∨ N areconceptstoo.

But are they? Concepts are supposed to capture thecommon properties of their instances (coherence). Whatcommonpropertiesdotheinstancesof¬M,orM ∨ N have?  Conceptsmusthave intensional properties sharedby all/

mostoftheirinstances,asopposedtonothavingproperties.  Accordingly,conceptssuchasANY(witheverythingasan

instance), and expressions such as ¬C and C1 ∨ C2 aresuspiciousconceptsforanyconceptualmodellinglanguage.

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Conceptualmodelsandontologies  In general, conceptual models may only include classes/

universals (e.g., conceptual schemas); but if they includetokens/particularstheyalsoneedtoincludetheirclasses.  Ontologies are shared computational models of

conceptuali-zations for a given domain (e.g., universities orbanks).  Every conceptual model adopts an ontology, but only

someconceptualmodelsareontologies.

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Conceptualmodelsasartifacts  Conceptualmodelsareartifacts,andlikeallartifacts,must

haverequirementsandstakeholders.  For example, say we want an enterprise model of your

Centre (CdI), covering strategic objectives, academicprogrammes, research activities, and academic staff; also itshould be ≥99% complete and 100% valid (no falseinformation!)  Whoarethestakeholders?MembersofCdIwithdifferent

areasofexpertise,alsomodellers.  Another example: Produce a specification for a meeting

scheduling system for CdI, given initial requirements R; thespecification should be complete, unambiguous, consistentandminimal(nounnecessaryrequirements).  Stakeholders: Members of CdI, requirements engineers,

modellers.

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Conceptualmodelsassocialartifacts  If conceptual models are computational models of

conceptual mental representations, whose mentalrepresentationsaretheycapturing?  An individual’s? Perhaps in Art, but not in Science and

Engineering.  In Computer Science conceptual models capture shared

mentalrepresentationsofagroupofstakeholders.  It follows that conceptualmodelling shouldbeadialectic

process involving stakeholders, and conceptual modelsshould come about through an argument amongstakeholders.

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Implicationsfortheresearchdiscipline  PerhapsthereshouldbeasuperconferenceonConceptual

Modelling that covers the areas of Conceptual Modelling,Knowledge Representation, Models, RequirementsModelling, Business Process Modelling, EnterpriseModelling.  For such a conference to succeed, it needs to have a

programme committee that can actually evaluate paperscoveringalltheseareas.

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Implicationsforresearch  Ideas that shaped and are still shaping Conceptual

Modelling have been debated for millennia in Philosophy.Payingattentiontothatrichhistoryofideasisusefulintwoways:

ü  It can tell us that some of our ideas won’t actuallywork,e.g.,conceptdefinitions;

ü  It can give us alternatives we should consider, e.g.,conceptsasprototypes.

  Looking at Philosophy andCognitive Science allowsus todefineconceptualmodelsintermsofthingsthatnoonehasever seen (conceptual mental representations), but areneverthelessacceptedasthingsthatactuallyexistandplayacriticalroleincognition.

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Conclusions  Conceptualmodelswereinitiallyproposedinseveralareas

of Computer Science as direct and natural models of adomain.  They constitute one of themost important contributions

ofComputerSciencetoScienceandotherdisciplinesinthatthey offer a subjectivemodelling technique, with potentialapplicationsinCognitiveScience,Sociology,Law,Economics/Managementandmore.  ThetopicofConceptualModellingshouldbeincludednot

only at University, but also Elementary and High SchoolcurriculabecauseitoffersanewkindofMathformodellingandreasoningabouttheworld.

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