An Introduction to Ontologies in OWL

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An Introduction to Ontologies in OWL

Bibliography The OWL GuideThe OWL OverviewDescription Logic slides from Enrico FranconiArtificial Intelligence A Modern Approach by Russel and Nordig

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What is an Ontology?

• A representation of terms and their interrelationships (OWL Overview)

• A formal conceptualization of the world

• Smart data

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Ontology Languages

• Typically introduce concepts, properties, relationships between concepts and constraints

• May be expressed with diagrams• ER Diagrams and UML Class Diagrams

are ontology languages• OWL (The Web Ontology Language) is

expressed in XML• OWL is a distributed ontology language

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The OWL Language

• February 10, 2004 OWL and RDF become W3C Recommendations

• See Jena from Hewlett-Packard Research for an existing Java API

• See Protégé-2000 at Stanford University for an existing OWL editor

• Big names in this space include Jim Hendler, and Debra McGuiness

• A large example can be found at http://www.mindswap.org/2003/CancerOntology/nciOncology.owl

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From the W3C

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The three sublanguages of OWL

• OWL Lite (decidable)

• OWL DL (Description Logic) (Decidable)

• OWL Full (Allows classes as instances)

• As we move from OWL Lite to OWL full we increase expressiveness and logical complexity.

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Decidability

• A proof procedure r is incomplete if there are true statements that the procedure cannot infer.

• Godel (1930’s) showed that, for first order logic, any statement entailed by a set of statements can be proved from the set. In other words, a proof procedure exists.

• In 1965, Robinson found the resolution method.

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Decidability

• But, entailment is semi-decidable. If a statement does not follow from the premises it may go on and on.

Resolution is complete

Premises

Statment S

If S follows the proofof S will emerge aftersome time.

If S does not followthe procedure may loop forever.

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OWL Lite is a Decidable Language

• A Class is a set of individuals

• The class Thing is the superclass of all OWL classes

• The class Nothing is a subclass of all OWL classes and has no individuals members

• Classes may be defined as subClasses of other classes

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Three classes that subclass Thing

<owl:Class rdf:ID=“Winery”/><owl:Class rdf:ID=“Region”/><owl:Class rdf:ID=“ConsumableThing”/>

These terms may be referred to from within thisDocument by ‘#Winery’,’ #Region’ and‘#ConsumableThing’.

Other ontologies may refer to these terms with‘SomeURI#Winery’, ‘SomeURI#Region’ and so on.

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Class Hierarchies built with subClassOf

<owl:Class rdf:ID=“PotableLiquid”> <rdfs:subClassOf rdf:resource = “#ConsumableThing” /> …</owl:Class>

<owl:Class rdf:ID=“EdibleThing”> <rdfs:subClassOf rdf:resource = “#ConsumableThing” /> …</owl:Class>

Deduction: If x is a PotableLiquidthen x is a ConsumableThing

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Wine and Pasta

<owl:Class rdf:ID=“Wine”> <rdfs:subClassOf rdf:resource =

“#PotableLiquid” /> …</owl:Class>

<owl:Class rdf:ID = “Pasta”<rdfs:subClassOf rdf:resource = “#EdibleThing” />…</owl:Class>

Deduction:

If x is Pasta then x isa ConsumableThing

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SweetFruit and NonSweetFruit

<owl:Class rdf:ID=“SweetFruit”> <!– food.xml--> <rdfs:subClassOf rdf:resource=“#EdibleThing”/></owl:Class>

<owl:Class rdf:ID=“NonSweetFruit”> <!– food.xml--> <rdfs:subClassOf rdf:resource=“#EdibleThing”/> …</owl:Class>

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Defining Individuals

<Region rdf:ID=“CentralCoastRegion”/>

Is identical to

<owl:Thing rdf:ID=“CentralCoastRegion”/>

<owl:Thing rdf:about=“#CentralCoatRegion”>

<rdf:type rdf:resource=“#Region”/>

</owl:Thing>

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Another individual

<owl:Class rdf:ID=“Grape”> <!– food.xml--> <rdfs:subClassOf rdf:resource=“#SweetFruit”/></owl:Class> <!– wine.xml --><owl:Class rdf:ID=“WineGrape”> <rdfs:subClassOf rdf:resource=“&food;Grape”/></owl:Class>

<WineGrape rdf:ID=“CabernetSauvignonGrape” />

Deduction: CabernetSauvignon is a SweetFruit

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So far we have…

Thing

Winery RegionConsumableThing

PotableLiquid EdibleThing

SweetFruit NonSweetFruit Pasta

Grape

WineGrape•CabernetSauvignonGrape

• CentralCoastalRegion

Wine

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So far we have …

• Classes

• Individuals

• We now need properties to state facts about classes and facts about individuals

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Properties

• Properties are binary relations

• A binary relation R from a set X to a set Y is a subset of the Cartesian product X x Y. If (x,y) ε R, we write xRy and say x is related to y.

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Binary Relations

Suppose the set X has members {a,b} andthe set Y has members {c,d,e}.

XxY = {(a,c),(a,d),(a,e),(b,c),(b,d),(b,e)}Let R = {(a,c),(b,e)}

Since (a,c) ε R and (b,e) ε R we write aRcand bRe.

Notice that a binary relation is a set of ordered pairs.

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The set {x ε X | (x,y) ε R for some y ε Y} is called the domain of R.

The domain of R = {(a,c),(b,e)} is {a,b}.

The set {y ε Y | (x,y) ε R for some x ε X} is called the range of R.

The range of R = {(a,c),(b,e)} is {c,e}.

Domain and Range

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Properties

• R is Transitive if and only if

xRy and yRz imply xRz

locateIn is transitive in the wine ontology

• R is Symmetric if and only if

xRy iff yRx

adjacentTo is symmetric in the wine ontology

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Properties

• R is Functional if and only if

xRy and xRz implies y = z

hasVintageYear is functional in the wine

ontology

• R1 and R2 are Inverse Properties if and only if

xR1y iff yR2x

hasMaker and producesWine are inverse

relations in the wine ontology

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OWL’s Property Hierarchy

• Thing is a superset of Property

• Property is a superset of ObjectProperty

• Property is a superset of DataProperty

• An ObjectProperty associates a class instance with another class instance.

• A DataProperty associates a class instance with a datatype value

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OWL’s Property Hierarchy Example

ThingMammal

Person• Mike• Sue

ObjectProperty

DataProperty

Property

hasRelative hasSibling

• (Mike,Sue)

hasAge• (Mike,23)

Indentation shows subsetrelationships.Set elements are markedwith dots.

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OWL Property Syntax

<owl:ObjectProperty rdf:ID=“locatedIn”>

<rdfs:domain

rdf:resource=“OWLURI#Thing”/>

<rdfs:range

rdf:resource=“#Region”/>

</owl:ObjectProperty>

“OWLURI” will actually appear as the official OWL URI.

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Adding pairs to locatedIn

<Region rdf:ID=“SantaCruzMountainsRegion”> <locatedIn rdf:resource=“#CaliforniaRegion”/></Region>

<CabernetSauvignon rdf:ID=

“SantaCruzMountainVinyardCabernetSauvignon”> <locatedIn

rdf:resource=“#SantaCruzMountainsRegion”/> …</CabernetSauvignon>

Can we make a deduction?

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locatedIn• locatedIn is defined as a set of ordered pairs. • Each pair must contain an owl:Thing (maybe a Region) followed by value from the set Region.

• For example: locatedIn = {(SantaCruzMountainsRegion, CaliforniaRegion), (SantaCruzMountainVinyardCabernetSauvignon, SantaCruzMountainsRegion)…}

• A deduction like the following is not yet possible… The Thing SantaCruzMountainVinyardCabernetSauvignon is locatedIn CaliforniaRegion

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locatedIn is Transitive

<owl:ObjectProperty rdf:ID=“locatedIn”> <rdf:type rdf:resource=“TransitiveProperty” /> <!– include an OWLURI -->

<rdfs:domain rdf:resource=“OWLURI#Thing”/> <rdfs:range rdf:resource=“#Region”/></owl:ObjectProperty>

• A deduction like the following is now possible… The Thing SantaCruzMountainVinyardCabernetSauvignon is locatedIn CaliforniaRegion

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Given the madeFromGrape property

<owl:ObjectProperty rdf:ID=“madeFromGrape”>

<rdfs:domain rdf:resource=“#Wine”/>

<rdfs:range rdf:resource=“#WineGrape”/>

</owl:ObjectProperty> madeFromGrape

(#Wine,#WineGrape)

(#Wine,#WineGrape)

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And…

<owl:Thing ref:ID=“LindemansBin65Chardonnay”>

<madeFromGrape rdf:resource=“#ChardonnayGrape”/>

<owl:Thing>

We can deduce that LindemansBin65Chardonnay is a Wine.

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Given a Property…

<owl:Class rdf:ID=“WineDescriptor”/>

<owl:Class rdf:ID=”WineColor”>

<rdfs:subClassOf rdf:resource=“WineDescriptor”/>

…

<owl:Class>

<owl:ObjectProperty rdf:ID=“hasWineDescriptor”>

<rdfs:domain rdf:resource=“#Wine”/>

<rdfs:range rdf:resource=“#WineDescriptor”/>

<owl:ObjectProperty>

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We can define a subproperty

<owl:ObjectProperty rdf:ID=“hasColor”>

<rdfs:subPropertyOf rdf:resource=“#hasWineDescriptor”/>

<rdfs:domain rdf:resource=“#Wine”/>

<rfds:range rdf:resource = “#WineColor” />

…

</owl:ObjectProperty>hasWineDescriptor

(#Wine,#WineDescriptor)(#Wine,#WineDescriptor)(#Wine,#WineDescriptor)(#Wine,#WineDescriptor)(#Wine,#WineColor)(#Wine,#WineColor)

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And make it functional.

<owl:ObjectProperty rdf:ID=“hasColor”>

<rdf:type rdf:resource=“&owl;FunctionalProperty”/>

<rdfs:subPropertyOf rdf:resource=“#hasWineDescriptor”/>

<rdfs:domain rdf:resource=“#Wine”/>

<rfds:range rdf:resource = “#WineColor” />

…

</owl:ObjectProperty>

hasWineDescriptor

(#Wine,#WineDescriptor)(#Wine,#WineDescriptor)(#Wine,#WineDescriptor)(#Wine,#WineDescriptor)(#Wine,#WineColor)(#Wine,#WineColor)

Now, for each Wine, therecan be at most one WineColor.

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<owl:Class rdf:ID=“Wine”> <rdfs:subClassOf rdf:resource = “&food;#PotableLiquid” /> <rdfs:subClassOf> <owl:Restriction> <owl:onProperty rdf:resource=“#madeFromGrape”/> <owl:minCardinality rdf:datatype= “&xsd;nonNegativeInteger”>1 </owl:minCardinalty> </owl:restriction> <rdfs:subClassOf> …</owl:Class>

Anonymous Classes

So, those Things that are in the PotableLiquid set that arealso in the set of things made from at least one grape are Wines. If we know that x isa Wine then we know it has atleast one madeFromGrapeproperty defined.

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A Wine Individual

<CabernetSauvignon rdf:ID= “SantaCruzMountainVinyardCabernetSauvignon”> <locatedIn rdf:resource=“#SantaCruzMountainsRegion”/> :</CabernetSauvignon>

This says nothing about what grape it’s made from. To find that outwe must look to the class CabernetSauvignon. There we learn allwines of this variety are madeFromGrape CabernetSauvignon.

So, individuals inherit properties and property values from their class.

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What does this mean?

<owl:Class rdf:ID="#Student">

<owl:intersectionOf rdf:parseType="Collection">

<owl:Class rdf:about="#Person"/>

<owl:Restriction>

<owl:onProperty rdf:resource="#enrolledIn"/>

<owl:minCardinality rdf:datatype=

"&xsd;nonNegativeInteger"> 1

</owl:minCardinality>

</owl:Restriction>

</owl:intersectionOf>

</owl:Class>

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And this?

<Student rdf:ID="John"> <friendOf> <Student rdf:resource="#Peter" /> </friendOf></Student>

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How about this one?<Student rdf:about=" http://www.student.org#DanielaRenuncio "> <owl:sameIndividualAs rdf:resource= "http://www.student.org#Daniela_de_Senna_Eyng_Renuncio"/></Student>