Ontology-Driven Conceptual Modelingguizzardi.panrepa.org/PUE-2016-p3.pdf · “rock kind” in a very simple, minimalist way (perhaps as synonymous with “rock class”), ignoring

Ontology-Driven Conceptual Modeling

Giancarlo Guizzardi

Ontology and Conceptual Modeling Research Group (NEMO) Federal University of Espírito Santo, Brazil

The Taxonomy of Animals inThe Celestial Emporium of

Benevolent Knowledge (Borges)• Those that belong to the emperor

• Those that resemble flies from a distance

• Those that have just broken a flower vase

• Embalmed ones

• Fabulous ones

“Those that resemble flies from a distance” is a logically possible way to group objects, but

it’s not how we naturally make sense of the world. No real language would have a noun for

such a category…Real nouns capture something deep; they refer to kinds of things that are thought to share deep properties…”

(Paul Bloom, How Pleasure Works, 2010)

“…As the evolutionary theorist Stephen Jay Gould put it, our classifications don’t just exist to avoid chaos, they are “theories about the

basis of natural order.”

(Paul Bloom, How Pleasure Works, 2010)

How$many$kinds$of$rock?

5

The Ontological Level: Revisiting 30 Years of Knowledge Representation 53

Fig. 1. Kinds of rocks (From [5])

proliferate easily, as soon as new attributes are added to the vocabulary. Hence they proposed a functional approach to knowledge representation designed to only answer “safe” queries that are about analytical relationships between terms, and whose answers are independent of the actual structure of the knowledge base, like “a large grey igneous rock is a grey rock”.

It is clear that, in this example, Brachman and colleagues understood the term “rock kind” in a very simple, minimalist way (perhaps as synonymous with “rock class”), ignoring the fact that, for many people, there are just three kinds of rocks, as taught at high school: Igneous, Metamorphic, and Sedimentary. On the other hand, two of the same authors, in an earlier paper on terminological competence in knowledge representation [6] stressed the importance of distinguishing an “enhancement mode transistor” (which is “a kind of transistor”) from a “pass transistor” (which is “a role a transistor plays in a larger circuit”).

So why was this distinction ignored? My own conclusion is that important issues related to the different ontological assumptions underlying our use of terms have been simply given up while striving for logical simplification and computational tractability. As a consequence, most representation languages, including “ontology languages” like OWL, do not offer constructs able to distinguish among terms having similar logical structure but different ontological implications. In our example, clearly “large rock” and “sedimentary rock” have the same logical structure, being both interpreted as the conjunction of two (primitive) logical properties; yet we tend to believe that there is something radically different between the two: why? To answer this question we have to investigate:

• the nature of the primitive properties “being a rock”, “being large”, and “being sedimentary”;

• the way they combine together in a structured term, while modifying each other.

Unfortunately, while current representation languages offer us powerful tools to build structured descriptions whose formal semantics is carefully controlled to provide efficient reasoning services, still no agreement has been reached concerning the need to adopt proper mechanisms to control the ontological commitments of structured

rock

igneous rock sedimentary rockmetamorphic rock

large rock grey rock

large grey igneous rock

grey sedimentary

rock

pet metamorphic rock

Brachman,)Fikes)and)Levesque,)1985

CATEGORIES*OF*OBJECT*TYPES

General$Terms$and$Common$Nouns

(i)$exactly$five$mice$were$in$the$kitchen$last$night$(ii)$the$mouse$which$has$eaten$the$cheese,$has$been$in$

turn$eaten$by$the$cat$


(i)$exactly$five$X$...$(ii)$the$Y$which$is$Z...$


(i)$exaclty$five$reds$were$in$the$kitchen$last$night$(ii)$the$red$which$has$...,$has$been$in$turn$...


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$Types

Whilst$the$characterizing$types$supply$only$a$principle$of$application$for$the$individuals$they$collect,$sortal$types$supply$both$a$principle$of$application$and$a$principle$of$identity$

The$Logical$Level∃x$Apple(x)$∧ Red(x)

The$Epistemological$Level

Apple

color = red

Red

sort = apple

The$Ontological$Level

Apple

color = red

Red

sort = apple

sortal universal characterizing Universal (mixin)

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$

* Every*Object*in*a*conceptual*model*(CM)*of*the*domain*

must*be*an*instance*of*a*class*representing*a*sortal*type*

*

Foundations $ Moreover,$since$NonTSortals$cannot$supply$a$principle$of$

identity$for$its$instances,$we$have$that,$all$NonTSortal$Types$in$the$model$must$be$represented$as$Abstract*Classes*

*

Unique$principle$of$Identity

X Y*Y$

18

PRINCIPLE OF IDENTITY

=

X Y*

Unique$principle$of$Identity

Y$


Foundations (2)$An$individual$cannot$obey$incompatible$principles$of$

identity

Distinctions$Among$$Categories$of$Object$Types

Object Type

Sortal Type Non-Sortal Type

Type

{Person,$Apple,$Student} {Insurable$Item,$Red}

Rigidity$(R+)

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)))*

$

R+(Person)*=def$□(∀x*Person(x)*→*□(Person(x)))$

e.g.,

AntiTRigidity$(R~)

A$types$T$is$antiTrigid$if$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$T:$

R~(T)*=def$□(∀x*T(x)*→*◊(¬T(x)))$

R~(Student)*=def$□(∀x*Student)*→*◊(¬Student(x)))$

e.g.,

ObjectType

Sortal Type Non-Sortal Type

Rigid Sortal Type Anti-Rigid Sortal Type

Type

Distinctions$Among$Categories$ of$Object$Types

{Person,$Organization}

{Insurable$Item}

{Student,$Teenager,$$FootballPlayer}

26


A$principle$of$identity$cannot$be$supplied$by$$either$of$these$two$antiTrigid$types,$

since$it$should$be$used$to$identify$individuals$$in$every$possible$situations!

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$they$inherit$a$principle$of$identity

P P’

S

…

Restriction$Principle

P P’

…

(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’

S

Uniqueness$Principle

$ (7)$G$and$S$cannot$have$incompatible$principles$of$identity$(by$2).$Therefore,$either:$

$ T$$ G$supplies$the$same$principle$as$S$and$therefore$G$is$the$ultimate$Sortal$

$ T$$ G$is$does$not$supply$any$principle$of$identity$(nonTsortal)$

$

P P’

…

G

…

S

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind


{Person,$Organization}

{Insurable$Item}


{Man,$Woman}

Foundations$Since$the$unique$principle$of$identity$supplied$by$a$Kind$is$

inherited$by$its$subclasses,$we$have$that:$A$NonTsortal$type$cannot$appear$in$a$conceptual$model$as$a$

subtype$of$a$sortal

Person

InsuredItem HeavyEntity



subtype$of$a$sortal

Person

InsuredItem HeavyEntity



subtype$of$a$sortal

Person

InsuredPerson HeavyPerson

HeavyEntityInsuredItem



subtype$of$a$sortal

Person

InsuredPerson HeavyPerson

HeavyEntityInsuredItem I1

I1 I1


inherited$by$its$subclasses,$we$have$that:$An$Object$in$a$conceptual$model$of$the$domain$cannot$

instantiate$more$than$one$ultimate$Kind

«kind»SocialBeing

«kind»Group

Organization

TheBeatles

instance of

«kind»SocialBeing

«kind»Group

Organization

TheBeatles

instance of

I1 I2

I1,$I2$

I1,$I2$

«kind»SocialBeing

«kind»Group

Organization

TheBeatles

instance of

«kind»SocialBeing

StaffOrganization

{John,Paul,George,Ringo}TheBeatles

instance of instance of

«constitution»

«kind»Group

Foundations$It$is$not$the$case$that$we$cannot$have$multiple$supertyping.$

Only$that$a$type$cannot$have$multiple$kinds$as$supertypes!

Foundations$It$is$important$to$emphasize$the$supertyping$is$a$modal$relation$

as$well,$i.e.,$if$A$is$supertype$of$B$then$A$is$necessarily$a$supertype$of$B

A

B

Ac

B

Fixed$ConfigurationSupertype(A,B)*=def$□(∀x*B(x)*→*A(x))$

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind

A$Kind$cannot$be$a$supertype$of$another$Kind

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind

A$subKind$cannot$be$a$supertype$of$a$kind

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind

A$subKind$type$MUST$have$as$a$supertype$$a$(unique)$Kind

Subkind$PartitionsIt$is$typical$that$subkinds$are$defined$in$structures$called$

Subkind$Partitions$These$are$not$always$partitions$in$the$strong$sense,$i.e.,$they$

defined$as$disjoint$but$rarely$complete$generalization$sets

«kind»Person

«subkind»Man «subkind»Woman

{disjoint ,complete }

Subkind$Partitions

«kind»Person

«subkind»Man «subkind»Woman


MalePerson

Female$Person

PERSON

These$partitions$are$the$same$In$every$possible$world!

SubkindsHowever,$subkinds$also$appear$outside$generalization$sets$as$

specializations$of$kinds

«kind»Organization

«subkind»EntertainmentOrganization

Subkinds


«subkind»EntertainmentOrganization

«subkind»NewsOrganization

«subkind»News&EntertainmentOrganization

This$only$makes$sense$if$there$are$genuine$(intrinsic$or$relational)$properties$to$be$defined$for$the$intersection$type

SubkindRemember$that$property$overriding$is$always$a$bad$idea$and$it$

is$always$caused$by$a$conceptual$modeling$mistake

declaredProfit:Currency

«subkind»NonProfitOrganization



SubkindRemember$that$property$overriding$is$always$a$bad$idea$and$it$

is$always$caused$by$a$conceptual$modeling$mistake


«subkind»ForProfitOrganization


«subkind»NonProfitOrganization

{disjoint,complete}

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind

An$AntiTRigid$type$MUST$have$as$a$supertype$$a$(unique)$Kind

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind

A$Kind$cannot$be$a$supertype$of$a$NonTSortal$Type

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind

A$Kind$cannot$be$a$supertype$of$a$NonTSortal$Type$in$fact,$since$all$sortals$will$inherit$a$principle$of$

Identity$from$a$Kind

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind

A$Sortal$Type$cannot$be$a$supertype$of$a$NonTSortal$Type

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind


{Person}

{Insurable$Item}


{Man,$Woman}

Relational$Dependence$(D+)

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$R:$

D+(T,P,R)*=def$□(∀x*T(x)*→*∃y$P(y)*∧*R(x,y))$

D+(Student,*School,*EnrolledOat)*=def$$

□(∀x*Student(x)*→*∃y$School*(y)*∧*EnrolledOat(x,y))$

e.g.,

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind Phase Role


{Person}

{Insurable$Item}

{Student,$$Husband}

{Man,$Woman} {Teenager,$$LivingPerson}

Roles

School«role»Student

*

enrolledTat

Roles

School«role»Student

*

The$Relational$property$in$this$case$is$part$of$$the$very$definition$of$the$Role:$

Student(x)$=def$Person(x)$∧ ∃y$School(y)$∧ enrolledTat(x,y)

en

enrolledTat

RolesDefined$as$a$(antiTrigid)$specialization$of$a$kind$such$that$the$

specialization$condition$is$a$relational$one$(correlated$with$derivation$by$participation)

«kind»Person

«role»Student «kind»School

1..* 1..*

enrolled-at

PERSON

STUDENT

SCHOOL

«kind»Person


1..* 1..*

enrolled-at

WORLD$W

PERSON

STUDENT

SCHOOL

«kind»Person


1..* 1..*

enrolled-at

WORLD$W’

PERSON

STUDENT

SCHOOL

«kind»Person


1..* 1..*

enrolled-at

WORLD$W’’

PhasesDefined$as$a$(antiTrigid)$specialization$of$a$kind$such$that$the$

specialization$condition$is$an$intrinsic$one$Phases$are$always$defined$in$a$soTcalled$Phase$Partition$Phase$Partitions$are$partitions$in$strong$sense,$i.e.,$they$are$

disjoint$and$complete$generalization$sets

Person

{disjoint,complete}

«phase»LivingPerson

«phase»DeceasedPerson

Person

{disjoint,complete}



LivingPerson

Deceased$Person

PERSON

WORLD$$W

Person

{disjoint,complete}



LivingPerson

Deceased$Person

PERSON

WORLD$W’

Person

{disjoint,complete}



LivingPerson

Deceased$Person

PERSON

WORLD$W’’

«kind»Person

«subkind»Man

«subkind»Woman




{disjoint ,complete}

Deceased$Person

PERSON

WORLD$W

Living$Person

Man

Woman

«kind»Person

«subkind»Man

«subkind»Woman





Deceased$Person

PERSON

WORLD$W’

Living$Person

Man

Woman

«kind»Person

«subkind»Man

«subkind»Woman





«kind»Person

«subkind»Man

«subkind»Woman




{disjoint ,complete }«phase»Child

«phase»Teenager

«phase»Adult


73

«kind»Person

«role»Customer

«role»Customer

«kind»Person


«role»Customer

«kind»Person


An$antiTrigid$type$cannot$be$a$supertype$of$a$Rigid$Type

Student

Person

x

Instance$of

WORLD$W

Student

Person

x

Instance$of

WORLD$W

Instance$of

Student

Person

x

Instance$of

WORLD$W’

Instance$of

RT

Since$Student$is$antiTrigid,$there$must$be$a$world$W’$such$that$x$is$not$an$instance$of$Student$in$W’

Student

Person

x

Instance$of

WORLD$W’

Instance$of

RT

But$since$Person$is$rigid$then$x$must$be$an$instance$of$Person$in$all$worlds,$

including$in$W’

R+

Student

Person

x

Instance$of

WORLD$W’

Instance$of

RT

But,$given$the$semantics$of$supertying,$we$have$that$in$all$worlds$(including$W’),$$

whoever$is$a$Person$is$a$Student

R+Instance$of

Student

Person

x

Instance$of

WORLD$W’

Instance$of

RT

We$run$into$a$logical$contradiction!

R+Instance$of

ObjectType

Sortal Type

Kind

Non-Sortal Type


Type

subKind Phase Role

An$antiTrigid$type$cannot$be$a$supertype$of$a$Rigid$Type

Different$Categories$of$Object$Types

Category*of*Type* Supply*

Identity*

Inherits*

Identity*

Rigidity* Dependence*

SORTAL* O* +*

«*kind*»* +* +* +* O*

«*subkind*»* O* +* +* O*

«*role*»* O* +* O* +*

«*phase*»* O* +* O* O*

NONOSORTAL* O* O*

K1

K2

K3

K4

K5

Kinds

K1

K2

K3

K4

K5

Anti-Rigid Sortals (Roles and Phases)

K1

K2

K3

K4

K5

Anti-Rigid Sortals (Roles and Phases)

Distinctions$Among$Object$Types

{Person} {Customer}{Student,$$Employee}

{Teenager,$$Living$Person}

ObjectType

Sortal Type

RoleKind

Non-Sortal Type


Phase

Rigid Non-Sortal Type

Type

Anti-Rigid Non-Sortal Type

subkind


ObjectType

Sortal Type

RoleKind

Non-Sortal Type


Phase


Type


subkind Category

{Person} {Physical$Object}{Student,$$Husband}

{Brazilian,$Man,$Woman}

{Teenager,$$LivingPerson}

Categories$are$rigid$nonTsortals$representing$necessary$(in$the$modal$sense)$features$of$entities$of$different$kinds$

Typically,$they$form$the$topTmost$layer$of$object$types$in$an$ontology$$

Categories$(IT,R+)

«kind»Person

«kind»Artificial Agent

«category»Rational Entity

{disjoint}

ARTIFICIAL$AGENT

PERSON

RATIONAL*ENTITY

Categories

Like$all$nonTsortals,$categories$are$always$defined$as$abstract$classes,$which$means$that$all$categories$must$have$at$least$a$kind$as$a$subtype

ObjectType

Sortal Type

RoleKind

Non-Sortal Type


Phase


Type


subkind Category

CategoriesA$kind$can$be$subtype$of$multiple$categories$and$a$category$can$

be$a$supertype$of$multiple$kinds$Since$all$kinds$are$disjoint$(otherwise$the$instances$in$their$

intersection$would$inherit$multiple$principles$of$identity),$all$subtypes$of$a$category$form$a$disjoint$generalization$set$

On$the$other$hand,$since$categories$represent$features$of$multiple$kinds,$they$are$very$seldom$complete$$

«category»PhysicalObject

«kind»Person «kind»Car «kind»Bridge

{disjoint}


{Person} {Customer}{Student,$$Employee}

{Teenager,$$Living$Person}

ObjectType

Sortal Type

RoleKind

Non-Sortal Type


Phase


Type


subkind Category RoleMixin




{Crime$Weapon}

RoleMixin(IT,RT,D+)RoleMixen$are$antiTrigid$and$relational$dependent$nonTsortals$

representing$contigent$(in$the$modal$sense)$features$of$entities$of$different$kinds$

As$all$NonTSortals,$RoleMixins$classify$entities$belonging$to$different$kinds$$

Like$all$nonTsortals,$categories$are$always$defined$as$abstract$classes

Roles$with$Disjoint$Allowed$Types

«role»Customer

Person Organization


«role»Customer

Person Organization

Participant

Person SIG

Forum

1..* *

participation

Roles$with$Disjoint$Admissible$Types

«roleMixin»Customer



«role»PersonalCustomer

«role»CorporateCustomer



«role»PersonalCustomer

Person Organization



«role»PrivateCustomer


«kind»Person

Organization

«kind»Social Being

«roleMixin»Participant

«role»IndividualParticipant

«role»CollectiveParticipant

«kind»Person

SIG

«kind»Social Being

Roles$with$Disjoint$Admissible$Types

«roleMixin»A

«role»B

F

D E

«role»C

1..*

1..*

Which$one$is$better?

Computer

hasTpart

MemoryDisk$Drive

Computer$Part

Memory$PartDisk$Part

Computer$Part

Disk$Drive Memory

Computer

hasTpart

by)Chris)Welty

The$Pattern$in$ORM

by)Terry)Halpin

Patterns$and$Metaphors

From$a$modeling$viewpoint,$patterns$can$be$seen$as$higherTgranularity$modeling$primitives$$$

Design$Patterns$are$the$modeling$counterpart$of$a$device$for$Structure$Transferability$capturing$a$domainTindependent$system$of$types$and$relations$that$offer$a$stardardized$solution$for$a$recurrent$problem$$$

RoleMixinsA$RoleMixin$cannot$be$a$superTtype$of$a$category,$in$fact,$

an$AntiTRigid$NonTSortal$type$cannot$be$a$supertype$of$a$rigid$one$

ObjectType

Sortal Type

RoleKind

Non-Sortal Type


Phase


Type


subkind Category RoleMixin

RoleMixin

PERSON

CUSTOMER

Personal$Customer

Corporate$Customer

WORLD$WORGANIZATION

Supplier

RoleMixin

PERSON

CUSTOMER

Personal$Customer

Corporate$Customer

WORLD$W’ORGANIZATION

Supplier

ObjectType

Sortal Type

RoleKind

Non-Sortal Type


Phase


Type

Non-Rigid Non-Sortal Type

subkind Category

RoleMixin

Anti-Rigid Non-Sortal Type Semi-Rigid Non-Sortal Type

Mixin





{Insurable$Item}

Modal$MetaTPropertiesWe$will$discuss$here$four$types$of$Ontological$MetaTProperties$

which$are$of$a$modal$nature

RIGIDITY NONORIGIDITY

ANTIORIGIDITY SEMIORIGIDITY

NonTRigidityAntiTRigidity$is$not$the$logical$negation$of$rigidity,$nonTrigidity$

is!$AntiTRigidity$is$stronger$than$that$as$a$logical$constraint

R+(T)*=def$□(∀x*T(x)*→*□(T(x)))*

$

RO(T)*=def$◊(∃xT(x) ∧◊¬T(x))*

$

Logical$Negation

Rigidity

NonTRigidity

NonTRigidity

AntiTRigidity$is$not$the$logical$negation$of$rigidity,$nonTrigidity$is!$AntiTRigidity$is$stronger$than$that$as$a$logical$constraint

R+(T)*=def$□(∀x*T(x)*→*□(T(x)))*

$

RO(T)*=def$◊(∃xT(x) ∧◊¬T(x))*

$

Logical$Negation

R~(T)*=def$□(∀x*T(x)*→*◊(¬T(x)))$AntiTRigidity

Rigidity

NonTRigidity

NonTRigidity

AntiTRigidity$is$not$the$logical$negation$of$rigidity,$nonTrigidity$is!$AntiTRigidity$is$stronger$than$that$as$a$logical$constraint

R+(T)*=def$□(∀x*T(x)*→*□(T(x)))*

$

R ¬(T)*=def$◊(∃xT(x) ∧◊¬T(x))*

$

Logical$Negation

RO(T)*=def$□(∀x*T(x)*→*◊(¬T(x)))$AntiTRigidity

Rigidity

NonTRigidity

R~*(T)*=def$RO(T)*∧ ¬R~(T)SemiTRigidity

Mixin(IT,R~)Mixins$are$semiTrigid$nonTsortals,$i.e.,$they$represent$features$

which$are$necessary$(in$the$modal$sense)$for$some$of$its$instances$but$contingent$to$others$$

SR(T)*=def*NR(T)*∧ ¬RO(T)*

Every$Mixin$must$be$a$supertype$of$a$rigid$type$as$well$as$a$supertype$of$a$NonTRigid$type$(typically$a$phase)

«mixin»InsuredItem

«kind»Car «phase»InsuredHouse

{disjoint }

«phase»NonInsuredHouse

«kind»House

{disjoint,complete}

MixinsMixins$represent$semiTrigid$features$of$multiple$kinds$Since$all$kinds$are$disjoint,$all$subtypes$of$a$mixin$form$a$

disjoint$generalization$set.$On$the$other,$like$in$the$case$of$categories,$these$generalization$sets$are$very$seldom$complete$$



{disjoint }


«kind»House

{disjoint,complete}

Mixin

HOUSE

CAR

INSURABLE**ITEM Insured$$

house

Uninsured$$house

WORLD$W

Mixin

HOUSE

CAR

INSURABLE**ITEM Insured$$

house

Uninsured$$house

WORLD$W’

Different$Categories$of$Object$Types

Category*of*Type* Supply*

Identity*

Identity* Rigidity* Dependence*

SORTAL* O* +*

«*kind*»* +* +* +* O*

«*subkind*»* O* +* +* O*

«*role*»* O* +* O* +*

«*phase*»* O* +* O* O*

NONOSORTAL* O* O*

«*category*»* O* O* +* O*

«*roleMixin*»* O* O* O* +*

«*mixin*»* O* O* ¬ O*

K1

K2

K3

K4

K5

Rigid Non-Sortals

K1

K2

K3

K4

K5

Anti-Rigid Non-Sortals

K1

K2

K3

K4

K5

Anti-Rigid Non-Sortals

METHODOLOGICAL*GUIDELINES

Ontological$MetaTProperties$of$Object$Types

These$ontological$metaTproperties$define$a$typology$of$Object$Types$that:$Define$a$formal$semantics$for$these$modeling$primitives$(present$in$a$number$of$current$approaches$–$ORM,$OntoClean)$but$which$have$been$defined$in$a$ad$hoc$manner$in$the$past$

Support$a$number$of$operational$semantics$with$important$consequences$to$a$number$of$implementation$technologies$(e.g.,$OWL,$OOP,$RDB),$but$also$for$verification$and$validation$technologies$

Define$methodological$guidelines$for$guiding$users$in$the$modeling$activity

Rigid$Backbone:$Kinds$and$SubKindsStart$by$identifying$the$rigid$backbone$of$your$model$This$is$the$taxonomic$structure$containing$only$kinds$and$their$

specializing$subkinds$Notice$that,$since$all$kinds$are$disjoint,$you$will$end$up$with$a$

forest$of$modelTtrees$This$Rigid$Backbone$defines$the$stable$structure$of$your$model$

and,$this$should$have$a$significant$impact$on$all$possible$implementations$of$your$model$regardless$of$the$implementation$technology$adopted$(e.g.,$ObjectTOriented$Technology,$Database$Technology,$RuleTBased$Systems,$Description$Logics$Systems)$

Rigid$Backbone:$Kinds$and$SubKindsSubkinds$frequently$appear$in$a$subkind$partition$with$

specializations$of$a$common$Kind.$This$partition$will$typically$be$disjoint$but$rarely$complete$Nonetheless,$it$is$interesting$to$identify$the$properties$which$

differentiate$the$subkinds$of$a$common$kind$as$well$as$to$identify$the$complementary$subkinds$belonging$to$the$same$partition

«kind»Person

«subkind»Man

«subkind»Woman


Methodological$Questions:$

Is$there$another$subkind$of$[Person]$which$is$complementary$to$Man?

Identify$AntiTRigid$Sortals

«kind»A

B

Candidate$AntiTRigid$Class


•Can$a$[A]$which$is$not$a$[B]$become$one?$(e.g.,$can$a$PERSON$who$is$not$a$FATHER$become$one?)$

•Can$a$[A]$which$is$[B]$cease$to$be$a$[B]?$(e.g.,$can$a$PERSON$who$is$a$FATHER$cease$to$be$a$FATHER?)

RolesRoles$are$always$(ultimately)$defined$as$specializations$of$kind$

via$a$relational$specialization$condition

«kind»A

B

AntiTRigid$Class


•Does$a$[A]$become$a$[B]$by$establishing$a$relation$to$another$type$of$entity?$(e.g.,$Does$a$PERSON$become$a$FATHER$by$establishing$a$relation$to$another$type$of$entity?)$

•What$would$be$name$of$that$defining$relation?$

•Find$out$the$cardinality$constraints$of$that$defining$relation

Roles

It$is$typical$that$this$type$will$also$be$a$role

«kind»Person

«role»Father «role»Offspring

1 1..*fatherhood

Minimum$cardinality$here$is$always$≥ 1

PhasesPhases$are$always$(ultimately)$defined$as$specializations$of$kind$

via$an$intrinsic$specialization$condition

«kind»A

B

AntiTRigid$Class


•Does$a$[A]$become$a$[B]$due$to$a$change$on$one$or$more$of$its$attribute$values?$(e.g.,$Does$a$PERSON$become$a$TEENAGER$due$to$a$change$on$one$or$more$of$its$attribute$values?)$

•Find$out$about$the$defining$attributes$and$associated$defining$values

Phases$are$always$defined$in$a$disjoint$and$complete$phase$partition

«kind»Person

«phase»Child

«phase»Teenager

«phase»Adult


Phases


•What$are$the$other$phases$complementary$to$[B]$in$which$[A]$can$be?$(e.g.,$What$are$the$other$phases$complementary$to$TEENAGER$in$which$a$PERSON$can$be?)$

•Find$out$about$the$defining$attributes$and$associated$defining$values$for$the$complementary$phases

Identify$NonTSortalsThe$direct$rule$of$thumb$for$identifying$nonTsortals$is$to$look$

for$types$that$can$have$instances$that$belong$to$multiple$kinds$

NonTSortals,$thus,$represent$common$features$that$are$shared$by$entities$of$multiple$kinds$

Are$these$features$necessary$or$contingent$ones?$

Categories$are$represent$necessary$features$shared$by$entities$of$multiple$kinds$

They$are$always$defined$a$supertype$of$multiple$rigid$types$forming$a$disjoint$partition$

Categories$(nonTsortals$in$general)$play$an$important$role$as$a$structuring$mechanism$in$conceptual$models$(particularly$in$large$ontologies)

Categories

Typically,$categories$are$identified$a*posteriori,$i.e.,$as$an$abstraction$mechanism$for$a$number$of$rigid$sortal$types$that$have$already$been$modeled$

The$definition$of$a$Category$them$amounts$to$abstract$these$shared$features$in$a$common$type$which$will$be$the$common$supertype$in$a$disjoint$generalization$set$relating$all$these$rigid$sortal$types$

«kind»Person

«kind»Artificial Agent

«category»Rational Entity

Categories

{disjoint}

Mixins$represent$features$shared$by$entities$of$multiple$kinds$which$are$necessary$for$some$of$its$instances$and$contingent$to$others$

Typically,$these$shared$features$are$identified$a*posteriori,$i.e.,$as$an$abstraction$mechanism$for$a$number$of$sortal$types$that$have$already$been$modeled$such$that$some$of$these$sortal$types$are$rigid$while$others$are$not$

The$definition$of$a$Mixin$them$amounts$to$abstract$these$shared$features$in$a$common$type$which$will$be$the$common$supertype$in$a$disjoint$generalization$set$relating$all$these$sortal$types$

Mixins

Again,$some$of$the$types$in$this$generalization$set$will$be$rigid$types$while$others$will$be$nonTrigid$ones$(typically$phases)

Mixins



{disjoint }


«kind»House

{disjoint,complete}

Role$Mixins$represent$contingent$and$relational$features$shared$by$entities$of$multiple$kinds$

Role$Mixins$typically$manifest$themselves$when$one$has$to$face$the$problem$of$Role*Modeling*with*Players*of*Multiple*Kinds***

In$other$words,$one$is$typically$faced$with$the$problem$of$having$a$candidate$role$(antiTrigid$sortal$with$an$identified$defining$relation)$but$which$can$be$played$by$entities$of$multiple$kinds

Role$Mixins

Decompose$the$candidate$Role$(which$is$in$fact$a$Role$Mixin)$in$a$number$of$specializing$Roles$such$that$each$of$these$subTroles$classify$only$entities$that$belong$to$the$same$Kind$$$

Connect$these$subTroles$with$their$corresponding$Kinds$via$specialization$relationships$$

The$role$mixin,$thus,$serve$as$an$abstraction$mechanism$for$all$these$subTroles$representing$its$shared$relational$features$(including$the$defining$relations)*

Role$Mixins

«roleMixin»A

«role»B

F

D E

«role»C

1..*

1..*

OntologyTDerived$Patterns

«roleMixin»A

«role»B

Obj.Type F

Sortal D Sortal E

«role»C

1..*

1..*

min≥1




«phase»Active Organization

«phase»Living Person

«role»Supplier

1..* 1..*

{disjoint , complete }






«role»Supplier

1..*

1..*

«phase»Deceased Person

«phase»Extinct Organization


{disjoint, complete}

«kind»Person



OntologyTDerived$Patterns

«roleMixin»A

«role»B

Obj.Type F

Sortal D Sortal E

«role»C

1..*

1..*

min≥1






«role»Supplier

1..* 1..*

{disjoint , complete }






«role»Supplier

1..*

1..*

«phase»Deceased Person

«phase»Extinct Organization



«kind»Person



http://nemo.inf.ufes.br/ [email protected]

Documents

Ontology-Driven Conceptual Modelingguizzardi.panrepa.org/PUE-2016-p3.pdf · “rock kind” in a very simple, minimalist way (perhaps as synonymous with “rock class”), ignoring