OWL Tutorial Final

8/3/2019 OWL Tutorial Final

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Ontology Web Language(OWL)

*Based on the Protg-OWL tutorial by Matthew Horridge et al.


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Outline

OWL executive summary

Components of OWL ontologies

Reasoning about OWL ontologies

Examples


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OWL Executive Summary

What is OWL

Web Ontology Language

A language to define vocabularies for modelling a world

A language to state facts (claims) about a world

W3C standard (http://www.w3.org/TR/owl-ref/)
http://www.w3.org/TR/owl-ref/http://www.w3.org/TR/owl-ref/http://www.w3.org/TR/owl-ref/http://www.w3.org/TR/owl-ref/


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Individuals

Represent entities or phenomena in a domain of interest e.g. Netherlands, My_car, Telematica_Instituut

John

JamesAmsterdam

London

Netherlands

Germany


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Classes

Person City

Country

An abstraction mechanism for grouping individuals with similarcharacteristics (e.g. Cars, Humans, Red things)

Defined by membership criteria (e.g. having a red color)

hence, two classes with the same members still may be different

We can explicitly state that an individual is a member of a class(e.g. My_car is a Red_Car)

Car

John

JamesAmsterdam

London

Netherlands

Germany


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Properties

hasBrother

hasCapitalCity

livesIn

livesIn

Can be defined independently from individuals

Define a binary relationship between two individuals orbetween an individual and a data value

name

PersonCity

CountryCar

John

JamesAmsterdam

London

Netherlands

Germany

25

hasAge


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Class Definition

A class can be defined

Axiomaticaly

i.e., by stating that the class exists e.g. Human, Car

By extension

i.e., by enumerating all individuals that belongto the class

e.g. {Belgium, Netherlands, Luxembourg}

By intension

i.e., by defining the membership criteria of theclass

e.g. having a red color


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Class Hierarchies

Person

Man

Father

Classes can be organised into a superclass-subclasshierarchy (also known as a taxonomy).

Father Man Person

If an individual is a member of a class, it is a member ofall its superclasses

A Man;we dont know

if it is a Father


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A class can be defined

as a subclass of an other class

Man Human.

a necessary condition to be a Man is to be Human

xMan x Human

as an equivalent (synonym) of an other class

MereMortal

Human. a necessary and sufficient condition to be

MereMortal is to be a Human

x MereMortal Human

Class Construction by IntensionSubclasses and Equivalent classes


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As an intersection of two or more classes

Human Male ( Man)a necessary and sufficient condition to be a Man is tobe Human and Male

As an union of two or more classes

Human Male

a necessary and sufficient condition to be a member ofthe class is to be Human or Male

Class Construction by IntentionIntersection and Union

Union of Human and Male


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Class Construction by IntensionComplement

As the complement of a class

Non_Human Humana necessary and sufficient condition to be aNon_Human is not to be a Human

Human

Non_Human

Either Human or Non_Humanwe dont know


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Thing and Nothing

Class owl:Thing ( T ) the necessary and sufficient condition to be a Thing is

always TRUE

All classes are subclasses of T

All individuals are members of T

Class owl:Nothing ( ) the necessary and sufficient condition to be Nothing is

always FALSE

is a subclass of all classes No individual is a member of


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Disjoint Classes

ManWoman

Classes that cannot have common members

Woman Man

A sufficient condition not to be a Man is to be a Woman and

vice versa.

a BallPoint


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Object and Datatype Properties

Object propertieslink individuals to individuals e.g. James hasFather George

Datatype propertieslink individuals to data values e.g. James hasAge 25

James

hasFather

George

hasAge

25


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Classes and Properties

Object properties relate an individual to an individual(i.e., members of Thing)

We can state that an object property can onlyrelate

members of class D (domain) to members of class R(range)

Likewise for a datatype property we can state that itsrange must be a primitive data type or a certain XML

schema type (xsd:int, xsd:string, etc)


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Existential Quantifier Restriction

$prop.ClassA

Defines an (anonymous) class X

necessary and sufficient condition to be member of X isto have at least oneproprelation to a member of ClassA.

$hasChild.Person


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Universal Quantifier Restriction

" prop.ClassA

Defines an (anonymous) class X

necessary and sufficient condition to be a memberof X is to have all(zero or more) prop relation to amember of ClassA

"drinks.Water


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Combining Existential and UniversalQuantifiers

Vegitarian $eats.VegitarianFood "eats.VegitarianFood

A vegitarian is someone who eats vegitarian food and only eatsvegitarian food

eats

eats

eats

VegitarianFood

Vegitarian


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Variations: hasValue Restrictions

prop.individualA

Defines an (anonymous) Class X

necessary and sufficient condition to be member of the Xis to have a prop relation to the individualA.


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Variation: Cardinality Restrictions

Defines a anonymous Class X.

necessary and sufficient conditions to be a member of X is tohave a defined number of prop relations to other individualsof a given class

Minimum cardinality restriction ()

Parent1.hasChild

Maximum cardinality restriction ()

LowBuilding 3.hasFloor

Exact cardinality restriction (=

)

Human =2.biologicalParents


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Compex Class Construction

Person Female $hasChild.(Person $hasChild.Person)

or

Woman Person Female

Parent Person $hasChild.Person Grandmother Woman $hasChild.Parent

A grandmother is a female person who has at least one childwho also has at least one child


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Inferred Relations

We can state that two individuals are related by property P

OWL allows us to infer other relations

Stated relation

Stated relation

Inferred relation


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Property Hierarchies

Like classes, properties can be more or less specific

if P Q then

x P y implies x Q y

hasDaughter hasChild

James

hasDaughter

Anna

hasChild


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Inverse Property

If Q is inverse property ofPthenx P y implies y Q x

hasParent inverse property hasChild

James

hasChild

Anna

hasParent


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Symmetric Property

Netherlands

bordersWith

Germany

borthersWith

If P is a symmetric property thenx P y implies y P x

borthersWith a symmetric property


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Transitive Property

If P is a transitive property then

x P y and y P z imply x P z

hasAncestor a transitive property

James

hasAncestor

George Peter

hasAncestor

hasAncestor


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Variation: ElementOf and subClass

If C D

x C implies x D

Father Man

James

Father Man


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Functional Property

James

hasBirthMother

Peggy

hasBirthMother

Mum

sameAs

Relation that is single (0 or 1) valued

If P is functional property then

x P a and x P b imply ab

If hasBirthMother is a functional property and JameshasBirthMother Peggy and James hasBirthMother

Mum then Peggy and Mum are the same individual


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Inverse Functional Property

Relation whose inverse is functional (i.e. the value uniqueidentifies the individual)

If P is inverse functional property then

x P id and y P id implies xy

If isBirthMotherOf is an inverse functional property andPeggy isBirthMotherOf James and MumisBirthMotherOf of James then Peggy and Mum are thesame individual

James

isBirthMotherOf

Peggy

isBirthMotherOf

Mum

sameAs


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Property-Level Reasoning

For all stated (black) relationships compute theimplied (red dashed) relationships

hasMother

Peggy James

hasFather

George Peter

hasFather

hasAncestor

hasChild

Anna

hasChild hasChild

hasAncestor

hasParent

hasAncestor

hasAncestor

hasAncestor

hasParent

hasChild

hasAncestor

hasParent hasAncestor

hasParent


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Class-level Reasoning Basic Concepts

Subsumption C is subsumed by D if the membership condition for Cimplies the membership condition for D (hence

C D and all members of C are members of D)

Satisfiability

C is unsatisfiable iff C is subsumed by

Equivalence

C and D are equivalent iff C is subsumed by D and D issubsumed by C

Disjointness C and D are disjoint iff the intersection of C and D is

subsumed by


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Individuals-level Reasoning Tasks

Consistency check

checks if an individual can exist in a given model

Realisation

given a partial description of an individual, finds the mostspecific class that describes it

Instance retrieval

finds all individuals that belong to a given class


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Example


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Queries

Find all rooms

(retrieve (?room)

(?room |Room|)

)


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Queries

Find all conference rooms with a beamer

(retrieve (?room)

(?room |ConferenceRoomWithABeamer|)

)

Documents

OWL Tutorial Final