Ontology-Driven Conceptual Modeling with Applications Giancarlo Guizzardi Computer Science Department Federal University of Espírito Santo (UFES), Brazil i* Internal Workshop Barcelona, Spain July, 2010

PROLOGUE

What is Conceptual Modeling? “the activity of formally describing some aspects of the physical and social world around us for purposes of understanding and communication…Conceptual modelling supports structuring and inferential facilities that are psychologically grounded. After all, the descriptions that arise from conceptual modelling activities are intended to be used by humans, not machines... The adequacy of a conceptual modelling notation rests on its contribution to the construction of models of reality that promote a common understanding of that reality among their human users.” John Mylopoulos

Formal Ontology To uncover and analyze the general categories and principles that describe reality is the very business of philosophical Formal Ontology Formal Ontology (Husserl): a discipline that deals with formal ontological structures (e.g. theory of parts, theory of wholes, types and instantiation, identity, dependence, unity) which apply to all material domains in reality.

What is Conceptual Modeling? “the activity of formally describing some aspects of the physical and social world around us for purposes of understanding and communication…Conceptual modelling supports structuring and inferential facilities that are psychologically grounded. After all, the descriptions that arise from conceptual modelling activities are intended to be used by humans, not machines... The adequacy of a conceptual modelling notation rests on its contribution to the construction of models of reality that promote a common understanding of that reality among their human users.” John Mylopoulos

The Chomskian Hypothesis I-Language vs. E-language –There is a universal common language competence (Universal Grammar/Mentalese) which is innate –There is a logical reason behind the fact that we are able to learn our first language, i.e., abstract a formal system capable of generating an infinite number of valid expressions: (i) only by being exposed to samples of this system; (ii) without meta- linguistic support which is available to second-language learners

OBJECT TYPES AND TAXONOMIC STRUCTURES

General Terms and Common Nouns (i) exaclty five mice were in the kitchen last night (ii) the mouse which has eaten the cheese, has been in turn eaten by the cat

General Terms and Common Nouns (i) exactly five X... (ii) the Y which is Z...

General Terms and Common Nouns (i) exaclty five reds were in the kitchen last night (ii) the red which has..., has been in turn...

General Terms and Common Nouns Both reference and quantification require that the thing (or things) which are refered to or which form the domain of quantification are determinate individuals, i.e. their conditions for individuation and numerical identity must be determinate

Sortal and Characterizing Universals Whilst the characterizing universals supply only a principle of application for the individuals they collect, sortal universals supply both a principle of application and a principle of identity

Foundations (1)We can only make identity and identification statements with the support of a Sortal, i.e., the identity of an individual can only be traced in connection with a Sortal type, which provides a principle of individuation and identity to the particulars it collects (Gupta, Macnamara, Wiggins, Hirsch, Strawson) Every Object in a conceptual model (CM) of the domain must be an instance of a CM-type representing a sortal.

Unique principle of Identity X Y

X Y

Foundations (2)An individual cannot obey incompatible principles of identity (Gupta, Macnamara, Wiggins, Hirsch, Strawson)

Distinctions Among Object Types {Person, Apple} {Insurable Item, Red}

Rigidity A type T is rigid if for every instance x of T, x is necessarily (in the modal sense) an instance of T. In other words, if x instantiates T in a given world w, then x must instantiate T in every possible world w’: R(T) = def □(  x T(x)  □(T(x)))

Anti-Rigidity A types T is anti-rigid if for every instance x of T, x is possibly (in the modal sense) not an instance of T. In other words, if x instantiates T in a given world w, then there is a possible world w’ in which x does not instantiate T: AR(T) =def □(  x T(x)   (  T(x)))

Distinctions Among Object Types {Person} {Insurable Item} {Student, Teenager}

Foundations (3)If an individual falls under two sortals in the course of its history there must be exactly one ultimate rigid sortal of which both sortals are specializations and from which they will inherit a principle of identity (Wiggins) PP’ S …

Restriction Principle PP’ S … (4)Instances of P and P’ must have obey a principle of identity (by 1) (5)The principles obeyed by the instances of P and P’ must be the same (by 2) (6)The common principle of identity cannot be supplied by P neither by P’

Uniqueness Principle (7) G and S cannot have incompatible principles of identity (by 2). Therefore, either: - G supplies the same principle as S and therefore G is the ultimate Sortal - G is does not supply any principle of identity (non-sortal) PP’ S … G …

Foundations A Non-sortal type cannot have direct instances. A Non-sortal type cannot appear in a conceptual model as a subtype of a sortal An Object in a conceptual model of the domain cannot instantiate more than one ultimate Kind (substance sortal).

Distinctions Among Object Types {Person} {Insurable Item} {Student, Teenager} {Man, Woman}

Relational Dependence A type T is relationally dependent on another type P via relation R iff for every instance x of T there is an instance y of P such that x and y are related via R: R(T,P,R) = def □(  x T(x)   y P(y)  R(x,y))

Distinctions Among Object Types {Person} {Insurable Item} {Student, Employee} {Teenager, Living Person}

A rigid type cannot be a subtype of a an anti-rigid type.

Subtyping with Rigid and Anti-Rigid Types 1.  x Person(x)  □Person(x) 2.  x Student(x)   Student(x) 3.□(Person(x)  Student(x)) 4.Person(John) 5.Student(John) 6.□Person(John) 7.□Student(John) 8.□Student(John)   Student(John) Person Student

Different Categories of Types Category of TypeSupply Identity Carry Identity RigidityDependence SORTAL-++/- « kind »+++- « subkind »-++- « role »-+-+ « phase »-+-- NON-SORTAL--+/-

Different Categories of Types Category of TypeSupply Identity IdentityRigidityDependence SORTAL-++/- « kind »+++- « subkind »-++- « role »-+-+ « phase »-+-- NON-SORTAL--+/~+/- « category »--+- « roleMixin »---+ « mixin »--~-

Distinctions Among Object Types {Person} {Customer} {Student, Employee} {Teenager, Living Person}

Roles with Disjoint Allowed Types

Roles with Disjoint Admissible Types

Roles with Disjoint Allowed Types

Roles with Disjoint Admissible Types

The Pattern in ORM by Terry Halpin

Different Categories of Types Category of TypeSupply Identity IdentityRigidityDependence SORTAL-++/- « kind »+++- « subkind »-++- « role »-+-+ « phase »-+-- NON-SORTAL--+/~+/- « category »--+- « roleMixin »---+ « mixin »--~-

Category

Mixin

PART-WHOLE RELATIONS

John part-of John’s Heart Person

John John’s Brain part-of

John part-of John’s Heart □((  Person,x) □(  (x)  (  !Heart,y)(y < x)))

John John’s Brain part-of □((  Person,x)(  !Brain,y) □(  (x)  (y < x)))

John part-of John’s Heart □((  Person,x) □(  (x)  (  !Heart,y)(y < x)))

part-of

Parts of Anti-Rigid Object Types “every boxer must have a hand” “every biker must have a leg”

De Re/De Dicto Modalities (i) The queen of the Netherlands is necessarily queen; (ii) The number of planets in the solar system is necessarily even.

Sentence (i) The queen of the Netherlands is necessarily queen:  x QueenOfTheNetherlands(x)  □(Queen(x)) □(  x QueenOfTheNetherlands(x)  Queen(x)) DE RE DE DICTO

Sentence (ii) The number of planets in the solar system is necessarily even:  x NumberOfPlanets(x)  □(Even(x))) □(  x NumberOfPlanets(x)  Even(x))) DE RE DE DICTO

The Boxer Example “every boxer must have a hand” “If someone is a boxer than he has at least a hand in every possible circumstance” DE RE DE DICTO “In any circumstance, whoever is boxer has at least one hand” □((  Boxer,x)(  Hand,y) □(  (x)  (y < x))) □((  Boxer,x) □(  (x)   Hand,y (y < x))) □((  Boxer,x)(  Hand,y) □(  (x)  Boxer(x)  (y < x)))

The Boxer Example “every boxer must have a hand” “If someone is a boxer than he has at least a hand in every possible circumstance” DE RE DE DICTO “In any circumstance, whoever is boxer has at least one hand” □((  Boxer,x)(  Hand,y) □(  (x)  (y < x))) □((  Boxer,x) □(  (x)   Hand,y (y < x))) □((  Boxer,x)(  Hand,y) □(  (x)  Boxer(x)  (y < x)))

Further Distinctions among Part-Whole relations –(i) specific dependence with de re modality (essential parts); –(ii) generic dependence with de re modality (mandatory parts); –(iii) specific dependence with de dicto modality (immutable parts). –ONLY RIGID TYPES CAN HAVE TRULY ESSENTIAL PARTS!

Anti-Rigid Types and Immutable Parts

Lifetime Dependency (Essential Parts)

The De Dicto equivalent of De Re formulae □((  Person,x)(  !Brain,y) □(  (x)  Person(x)  (y < x))) □((  Person,x) □(  (x)  Person(x)  (  !Heart,y)(y < x)))

General Schemata for Immutable Parts

John part-of

John part-of John’s Brain part-of

Summary of Visual Patterns

Tool Support The underlying algorithm merely has to check structural properties of the diagram and not the content of involved nodes

Colorless green ideas sleep furiously Chomsky, 1957

House (Episode 2-10) House: Hi, I'm Gregory House; I'm your attending physician, your wife's not there, start talking. Fletcher: They took my stain! I couldn't tackle the bear, they took my stain.

ATL Transformation Alloy Analyzer + OntoUML visual Plugin Simulation and Visualization

The alternative to philosophy is not “non- philosophy” but bad philosophy! A scientific field can either develop and make explicit its foundations or remain oblivious to its inevitable and often ad hoc ontological commitments.

Acknowledgements This research is funded by the Brazilian Research Funding Agencies FAPES (grant number /09) and CNPq (grants number /2009-6)

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