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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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