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OWL: Web Ontologies

OWL: Web Ontologies. Matthew Yau C.Y.Yau@warwick.ac.uk. Reminder on Ontologies. An ontology is a formal, explicit specification of a shared conceptualisation.

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OWL: Web Ontologies

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  1. OWL:Web Ontologies Matthew Yau C.Y.Yau@warwick.ac.uk

  2. Reminder on Ontologies An ontology is a formal, explicit specification of a shared conceptualisation. • A conceptualisation refers to an abstract model of some phenomenon in the world which identifies the relevant concepts of that phenomenon. • Explicit means that the type of concepts used and the constraints on their use are explicitly defined. • Formal refers to the fact that the ontology should be machine understandable, i.e. the machine should be able to interpret the semantics of the information provided. • Shared reflects the notion that an ontology captures consensual knowledge, that is, it is not restricted to some individual, but accepted by a group.

  3. RDF Schema and Ontologies • Can define Classes and Properties • Using: <rdfs:Class ...>...</rdfs:Class> • Using: <rdfs:Property ...>...</rdfs:Property> • Can identify Individuals as members of classes • Using: <rdf:type ... />. • Can identity the domain and range of a property. • Using: <rdfs:domain ...> • Using: <rdfs:range ...> • Can identity subclasses and subproperties • Using: <rdfs:subClassOf ...>...</rdfs:subClassOf> • Using: <rdfs:subPropertyOf ...>...</rdfs:subPropertyOf>

  4. RDF Schema Problems • there are lot of relationships we would like to add which RDF Schema does not allow us to say: That two classes are disjoint - they have no members in common • e.g. Cats and Dogs That properties are Inverses of each other - that is one property is the other "backwards": • e.g. hasChild and hasParent That one class is formed by taking union of two other classes. • e.g. UniversityMembers is the combination of Staff and Students That two classes are the same. • e.g. the class Humans is the same as the class People

  5. OWL: Three variants on OWL • OWL provides three increasingly expressive sublanguages designed for use by specific communities of implementers and users. • OWL Lite: • OWL DL: • OWL Full

  6. OWL: Namespaces • As we are using RDF as the basis of OWL, we start with a rdf:RDF element, and a series of Namespace declarations. • <rdf:RDF xmlns ="http://example.org/walkthru-in-owl#" xmlns:oex ="http://example.org/walkthru-in-owl#" xmlns:owl ="http://www.w3.org/2002/07/owl#" xmlns:rdf ="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#" xmlns:xsd ="http://www.w3.org/2000/10/XMLSchema#">

  7. OWL: Starting the Ontology • This give metadata about the ontology. <owl:Ontology rdf:about=""> <owl:versionInfo>walkthru-in- owl.v2.0.0</owl:versionInfo> <owl:priorVersion rdf:resource="http://example.org/wal kthru-in-owl-v1"></owl:priorVersion> <rdfs:comment> An example ontology, with data types taken from XML Schema </rdfs:comment> <owl:imports rdf:resource="..."/> <rdfs:label>Walkthru Ontology</rdfs:label> </owl:Ontology>

  8. OWL: Defining Classes • Classes are defined in a very similar manner to RDF Schema classes. <owl:Class rdf:ID="Animal"> <rdfs:label>Animal</rdfs:label> <rdfs:comment> This is the class of animals. </rdfs:comment> </owl:Class>

  9. OWL: Defining Classes • owl:Class is defined as a subclass of rdfs:Class <rdfs:Class rdf:ID="Class"> <rdfs:label>Class</rdfs:label> <rdfs:comment>The class of all "object" classes</rdfs:comment> <rdfs:subClassOf rdf:resource="http://www.w3.org/2000/01/rdf-schema#Class" /> </rdfs:Class>

  10. OWL: Class Thing and Nothing <Class rdf:ID="Thing"> <rdfs:label>Thing</rdfs:label> <rdfs:comment> The most general (object) class in DAML. This is equal to the union of any class and its complement. </rdfs:comment> <unionOf rdf:parseType="Collection"> <rdfs:Class rdf:about="#Nothing"/> <rdfs:Class> <complementOf rdf:resource="#Nothing"/> </rdfs:Class> </unionOf> </Class> <Class rdf:ID="Nothing"> <rdfs:label>Nothing</rdfs:label> <rdfs:comment>the class with no things in it.</rdfs:comment> <complementOf rdf:resource="#Thing"/> </Class>

  11. OWL: Defining SubClasses • As OWL classes are also RDF classes, we can use RDF Schema's subclassing mechanism <owl:Class rdf:ID="Male"> <rdfs:subClassOf rdf:resource="#Animal"/> </owl:Class> <owl:Class rdf:ID="Man"> <rdfs:subClassOf rdf:resource="#Person"/> <rdfs:subClassOf rdf:resource="#Male"/> </owl:Class>

  12. OWL: disjointWith Axiom • Class descriptions form the building blocks for defining classes through class axioms. <owl:Class rdf:ID="Female"> <rdfs:subClassOf rdf:resource="#Animal"/> <owl:disjointWith rdf:resource="#Male"/> </owl:Class> • NOTE: OWL Lite does not allow the use of owl:disjointWith

  13. OWL: Defining Individuals • Recall that in the OIL example, we provided individuals. • Can simply do the same in OWL - as in RDF: <Man rdf:ID="Peter" /> <Man rdf:ID="Ian"/> This just says that Peter and Ian are objects in the class Man. The first is equivalent to saying: <owl:Thing rdf:ID="Peter" /> <owl:Thing rdf:about="#Peter"> <rdf:type rdf:resource="#Man"/> </owl:Thing>

  14. OWL: sameAs Individuals • OWL can allow us to assert that individuals are the same • Use the owl:sameAs property <Man rdf:ID="Peter" /> <Man rdf:ID="MrSmith"> <owl:sameAs rdf:resource="#Peter" /> </Man>

  15. OWL: Enumerated Classes • OWL DL (not OWL Lite) can provide Classes of enumerated individual values. <owl:Class rdf:ID="Height"> <owl:oneOf rdf:parseType="owl:collection"> <Height rdf:ID="short"/> <Height rdf:ID="medium"/> <Height rdf:ID="tall"/> </owl:oneOf> </owl:Class>

  16. OWL: Defining Properties • OWL allows us to define two sorts of Properties: • Datatype properties • Object properties

  17. OWL: Defining DataType Properties • DataType Properties relate Classes with Datatypes (e.g. literals defined in XML Schema) <owl:DatatypeProperty rdf:ID="age"> <rdfs:comment> age is a DatatypeProperty whose range is xsd:nonNegativeInteger. </rdfs:comment> <rdfs:range rdf:resource="http://www.w3.org/2000/10/XMLSchema#nonNegativeInteger"/> </owl:DatatypeProperty>

  18. OWL: Object Properties • To define Object Properties, we use owl:ObjectProperty. Again similar to RDF Schema properties, with domains and ranges: <owl:ObjectProperty rdf:ID="hasParent"> <rdfs:domain rdf:resource="#Animal"/> <rdfs:range rdf:resource="#Animal"/> </owl:ObjectProperty> • Domain and range information can be used to infer type information <owl:Thing rdf:ID="Fred"> <hasParent rdf:resource="#Ian" /> </owl:Thing> • Allows us to deduce that Fred is an Animal

  19. OWL: Object Properties • As another example, we define a property called hasHeight <owl:ObjectProperty rdf:ID="hasHeight"> <rdfs:range rdf:resource="#Height"/> </owl:ObjectProperty> • We don't specify a domain, so this can be the height of any "Thing" • The following is the formal defintion of ObjectProperty from the OWL standard.

  20. OWL: Object Properties • The following is the formal defintion of ObjectProperty from the OWL standard <rdfs:Class rdf:ID="ObjectProperty"> <rdfs:label>ObjectProperty</rdfs:label> <rdfs:comment>if P is an ObjectProperty, and P(x, y), then y is an object. </rdfs:comment> <rdfs:subClassOf rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property" /> </rdfs:Class>

  21. OWL: SubProperties • Subproperties again are similar to RDF Schema: <owl:ObjectProperty rdf:ID="hasFather"> <rdfs:subPropertyOf rdf:resource="#hasParent"/> <rdfs:range rdf:resource="#Male"/> </owl:ObjectProperty>

  22. OWL: Property Characteristics • Property Characteristics specify the nature of properties, which can then be used to enhance the reasoning over the property. • We can specify what they mean by considering triples, that is we consider the triples (x P y) for the property P.

  23. OWL: Symmetric Property • A symmetric property is one which can be "switched around" and still remain within the property • That is, for a symmetric property P, if triple (x,P,y) then triple (y,P,x) <owl:SymmetricProperty rdf:ID="isMarriedTo"> <rdfs:domain rdf:resource="#Person"/> <rdfs:range rdf:resource="#Person"/> </owl:SymmetricProperty> • So if we have: Mary isMarriedTo Adam • Then since isMarriedTo is Symmetric, then Adam isMarriedTo Mary

  24. OWL: Transitive Property • That is P is a transitive property, if triple (x,P,y) and triple (y,P,z), then triple (x,P,z): <owl:TransitiveProperty rdf:ID="hasAncestor"> <rdfs:label>hasAncestor</rdfs:label> </owl:TransitiveProperty> <owl:TransitiveProperty rdf:ID="descendant"/>

  25. OWL: Transitive Property • So if we have: Mary hasAncestor Anne . Anne hasAncestor Adam . • Then since hasAncestor is Transitive, then Mary hasAncestor Adam. • TransitiveProperty is a sub-property of ObjectProperty

  26. OWL: Functional Property • So P is a FunctionalProperty if triple (x,P,y) and triple (x,P,z), then (y = z). <owl:FunctionalProperty rdf:ID="hasMother"> <rdfs:subPropertyOf rdf:resource="#hasParent"/> <rdfs:range rdf:resource="#Female"/> </owl:FunctionalProperty>

  27. OWL: Functional Property • So if we have: Mary hasMother MrsRobinson. Mary hasMother Anne. • Then since hasMother is Functional, then : Anne owl:sameAs MrsRobinson.

  28. OWL: Functional Property • We can also say that Datatype properties are functional. <owl:DatatypeProperty rdf:ID="age"> <rdfs:comment> age is also a FunctionalProperty (can only have one age) </rdfs:comment> <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/> <rdfs:range rdf:resource="http://www.w3.org/2000/10/XMLSchema#nonNegativeInteger"/> </owl:DatatypeProperty>

  29. OWL: Inverse Functional Property • So P is a InverseFunctionalProperty if triple (x,P,y) and triple (z,P,y), then (x = z). : <owl:InverseFunctionalProperty rdf:ID="isMarriedTo"/> • We can also say that Datatype properties are inverse functional. <owl:DatatypeProperty rdf:ID="studentNumber"> <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/> <rdfs:range rdf:resource="http://www.w3.org/2000/10/XMLSchema#nonNegativeInteger"/> </owl:DatatypeProperty>

  30. OWL: Inverse Functional Property • So if we have: Mary studentNumber 87324. MsSmith studentNumber 87324. • Then since studentNumber is Inverse Functional, then : Mary owl:sameAs MsSmith. • If the Ontology demands that they are different objects, then there is a contradiction.

  31. OWL: Inverse Property • if have the triple (x,P,y), then triple (y,Q,x)): <owl:ObjectProperty rdf:ID="hasChild"> <owl:inverseOf rdf:resource="#hasParent"/> </owl:ObjectProperty> • So if we have: Mary hasChild Adam . • Then since hasChild and hasParent are inverse properties, then : Adam hasParent Mary .

  32. OWL: Property Restrictions • A slightly tricky example - as this is recursive. <owl:Class rdf:ID="Person"> <rdfs:subClassOf rdf:resource="#Animal"/> <rdfs:subClassOf> <owl:Restriction> <owl:onProperty rdf:resource="#hasParent"/> <owl:allValuesFrom rdf:resource="#Person"/> </owl:Restriction> </rdfs:subClassOf> </owl:Class>

  33. OWL: Property Restrictions - Some Values From • As well as using allValuesFrom, we can also construct restrictions where at least one value of a domain is from a particular class <owl:Class rdf:ID="Carnivore"> <rdfs:subClassOf rdf:resource="#Animal"/> <rdfs:subClassOf> <owl:Restriction> <owl:onProperty rdf:resource="#eats"/> <owl:someValuesFrom rdf:resource="#Animal"/> </owl:Restriction> </rdfs:subClassOf> </owl:Class>

  34. OWL: Cardinality Restrictions • Can also use restriction to set the number of times a property can occur on a class instance: <owl:Class rdf:about="#Person"> <rdfs:subClassOf> <owl:Restriction> <owl:onProperty rdf:resource="#hasFather"/> <owl:cardinality rdf:datatype="&xsd;nonNegativeInteger">1</owl:cardinality> </owl:Restriction> </rdfs:subClassOf> </owl:Class>

  35. OWL: Cardinality Restrictions • Can also have minCardinality and maxCardinality <owl:Class rdf:about="#Person"> <rdfs:subClassOf> <owl:Restriction> <owl:onProperty rdf:resource="#hasSpouse"/> <owl:maxCardinality rdf:datatype="&xsd;nonNegativeInteger">1</owl:maxCardinality> </owl:Restriction> </rdfs:subClassOf> </owl:Class>

  36. OWL: Defining Classes by Value • OWL DL (not OWL Lite) allows us to specify classes based on the existence of particular property values. • TallThing is within the class of things whose hasHeight has the value tall: <owl:Class rdf:ID="TallThing"> <owl:subClassOf > <owl:Restriction> <owl:onProperty rdf:resource="#hasHeight"/> <owl:hasValue rdf:resource="#tall"/> </owl:Restriction> </owl:subClassOf> </owl:Class>

  37. OWL: Equivalent Classes and Properties • OWL provides constructs to say that Classes and Properties can be equivalant. • We can set classes to be equivalent. <owl:Class rdf:ID="HumanBeing"> <owl:EquivalentClass rdf:resource="#Person"/> </owl:Class> • We can declare that two properties are the same: <owl:ObjectProperty rdf:ID="hasMum"> <owl:EquivalentProperty rdf:resource="#hasMother"/> </owl:ObjectProperty>

  38. OWL: Equivalent Classes and Properties • These constructs can be used to map different Ontologies together. <owl:Class rdf:ID="MyPerson"> <owl:EquivalentClass rdf:resource="foaf:Person"/> </owl:Class>

  39. OWL: Equivalent Classes and Properties • Also, we can combine with a property restriction to say that the new class is exactly the restricted class. <owl:Class rdf:about="#Carnivore"> <rdfs:EquivalentClass> <owl:Restriction> <owl:onProperty rdf:resource="#eats"/> <owl:allValuesFrom rdf:resource="#Animal"/> </owl:Restriction> </rdfs:EquivalentClass> </owl:Class>

  40. OWL: Union • Thus Unions e.g. People are made up of exactly Men and Women: <owl:Class rdf:about="#Person"> <rdfs:comment>every person is a man or a woman</rdfs:comment> <owl:unionOf rdf:parseType="owl:collection"> <owl:Class rdf:about="#Man"/> <owl:Class rdf:about="#Woman"/> </owl:unionOf> </owl:Class>

  41. OWL: Intersection • Similarly for Intersection e.g. a tall man is a tall thing which is also a man: <owl:Class rdf:ID="TallMan"> <owl:intersectionOf rdf:parseType="owl:collection"> <owl:Class rdf:about="#TallThing"/> <owl:Class rdf:about="#Man"/> </owl:intersectionOf> </owl:Class>

  42. OWL: Complementary Classes • Complements e.g. Inanimate objects are the things which are not living: <owl:Class rdf:ID="InanimateThing"> <owl:complementOf rdf:parseType="owl:collection"> <owl:Class rdf:about="#LivingThing"/> </owl:complementOf> </owl:Class>

  43. OWL: Defining Classes using these operations • Can be used to give the necessary and sufficient condition for a class. • e.g. Married People are People who are Married: <owl:Class rdf:ID="MarriedPerson"> <owl:intersectionOf rdf:parseType="owl:collection"> <owl:Class rdf:about="#Person"/> <owl:Restriction > <owl:onProperty rdf:resource="#hasSpouse"/> <owl:cardinality rdf:datatype="&xsd;nonNegativeInteger">1</owl:cardinality> </owl:Restriction> </owl:intersectionOf> </owl:Class>

  44. OWL: Defining Classes using these operations • e.g. People are not Cats: <owl:Class rdf:ID="Cat"> <rdfs:comment>no cat is a person</rdfs:comment> <rdfs:subClassOf> <owl:Class> <owl:complementOf rdf:resource="#Person"/> </owl:Class> </rdfs:subClassOf> </owl:Class>

  45. OWL: User Defined DataTypes • By combining with XML Schema DataTypes we can make more precise definitions of the values that Datatype properties can have, in the XML Schema. <xsd:simpleType name="over17"> <xsd:restriction base="xsd:positiveInteger"> <xsd:minInclusive value="18"/> </xsd:restriction> </xsd:simpleType>

  46. OWL: User Defined DataTypes • And in the OWL file: <owl:Class rdf:ID="Adult"> <owl:Restriction> <owl:onProperty rdf:resource="#age"/> <owl:allValuesFrom rdf:resource= "http://example.org/walkthru-in-owl#over17"/> </owl:Restriction> </owl:Class>

  47. OWL: Defining Instances • Thus to redefine the Individuals we had earlier, with some additional properties: <Person rdf:ID="Peter"> <shoesize>9.5</shoesize> <age>46</age> <shirtsize>15</shirtsize> </Person> <Person rdf:ID="Ian"> <shoesize>14</shoesize> <age>37</age> <shirtsize><xsd:string rdf:value="12"/></shirtsize> </Person>

  48. OWL-QL • OWL-QL (OWLQuery Language) • a query language for OWL • based on DQL (DAML Query Lang.) • supports query-answering dialogues

  49. Basic Queries a query pattern (required) a must-bind variables list a may-bind variables list a don’t bind variables list an answer pattern a query premise an answer KB pattern an answer bundle size bound

  50. A simple OWL-QL query 1 • If C1 is a Seafood Course and W1 is a drink of C1,what color is W1? P: (type C1 Seafood-Course) (drink C1 W1) Q: (has-color W1 ?x) V: must-bind ?x AP: drink ?x Wine with Seafoood KB: http://somewhere.com/wine.owl A: drink White Wine with Seafood

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