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An Introduction to Ontologies in OWL

An Introduction to Ontologies in OWL. Bibliography The OWL Guide The OWL Overview Description Logic slides from Enrico Franconi Artificial Intelligence A Modern Approach by Russel and Nordig. What is an Ontology?. A representation of terms and their interrelationships (OWL Overview)

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An Introduction to Ontologies in OWL

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  1. An Introduction to Ontologies in OWL Bibliography The OWL Guide The OWL Overview Description Logic slides from Enrico Franconi Artificial Intelligence A Modern Approach by Russel and Nordig Internet Technologies

  2. What is an Ontology? • A representation of terms and their interrelationships (OWL Overview) • A formal conceptualization of the world • Smart data Internet Technologies

  3. 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 Internet Technologies

  4. 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 Internet Technologies

  5. From the W3C Internet Technologies

  6. 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. Internet Technologies

  7. 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. Internet Technologies

  8. Decidability • But, entailment is semi-decidable. If a statement does not follow from the premises it may go on and on. If S follows the proof of S will emerge after some time. Resolution is complete Premises If S does not follow the procedure may loop forever. Statment S Internet Technologies

  9. 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 Internet Technologies

  10. 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 this Document by ‘#Winery’,’ #Region’ and ‘#ConsumableThing’. Other ontologies may refer to these terms with ‘SomeURI#Winery’, ‘SomeURI#Region’ and so on. Internet Technologies

  11. 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 PotableLiquid then x is a ConsumableThing Internet Technologies

  12. 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 is a ConsumableThing Internet Technologies

  13. 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> Internet Technologies

  14. 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> Internet Technologies

  15. 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 Internet Technologies

  16. So far we have… Thing Winery Region ConsumableThing • CentralCoastalRegion PotableLiquid EdibleThing SweetFruit NonSweetFruit Pasta Wine Grape WineGrape • CabernetSauvignonGrape

  17. So far we have … • Classes • Individuals • We now need properties to state facts about classes and facts about individuals Internet Technologies

  18. 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. Internet Technologies

  19. Binary Relations Suppose the set X has members {a,b} and the 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 aRc and bRe. Notice that a binary relation is a set of ordered pairs. Internet Technologies

  20. Domain and Range 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}. Internet Technologies

  21. 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 Internet Technologies

  22. 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 Internet Technologies

  23. 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 Internet Technologies

  24. OWL’s Property Hierarchy Example Thing Mammal Indentation shows subset relationships. Set elements are marked with dots. Person • Mike • Sue Property ObjectProperty DataProperty hasRelative hasSibling • (Mike,Sue) hasAge • (Mike,23) Internet Technologies

  25. 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. Internet Technologies

  26. 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? Internet Technologies

  27. 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 Internet Technologies

  28. 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 Internet Technologies

  29. 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) Internet Technologies

  30. And… <owl:Thing ref:ID=“LindemansBin65Chardonnay”> <madeFromGrape rdf:resource=“#ChardonnayGrape”/> <owl:Thing> We can deduce that LindemansBin65Chardonnay is a Wine. Internet Technologies

  31. 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> Internet Technologies

  32. 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) Internet Technologies

  33. 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, there can be at most one WineColor. Internet Technologies

  34. Anonymous Classes <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> So, those Things that are in the PotableLiquid set that are also in the set of things made from at least one grape are Wines. If we know that x is a Wine then we know it has at least one madeFromGrape property defined. Internet Technologies

  35. 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 out we must look to the class CabernetSauvignon. There we learn all wines of this variety are madeFromGrape CabernetSauvignon. So, individuals inherit properties and property values from their class. Internet Technologies

  36. 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> Internet Technologies

  37. And this? <Student rdf:ID="John"> <friendOf> <Student rdf:resource="#Peter" /> </friendOf> </Student> Internet Technologies

  38. 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> Internet Technologies

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