246 CHAPTER 11 Basic OWL Now we can define ChildOfShakespeare to be (equivalent to) the class of all individuals who are b:memberOf b:Shakespeares_Children, using an owl:hasValue restriction: b:ChildOfShakespeare a owl:Class; rdfs:label "Child of Shakespeare"; owl:equivalentClass [a owl:Restriction; owl:hasValue b:Shakespeares_Children; owl:onProperty b:memberOf ]. Let's follow the progression of Shakespeare's children through this inference. From Figure 11.11, we begin with three triples: b:Shakespeares_Children foaf:member b:Hamnet. b:Shakespeares_Children foaf:member b:Judith. b:Shakespeares_Children foaf:member b:Susanna. By the semantics of owl:inverseOf, we can infer b:Hamnet b:memberOf b:Shakespeares_Children. b:Judith b:memberOf b:Shakespeares_Children. b:Susanna b:memberOf b:Shakespeares_Children. Therefore, all three are also members of the restriction defined previously, so we can conclude that b:Hamnet rdf:type b:ChildOfShakespeare. b:Judith rdf:type b:ChildOfShakespeare. b:Susanna rdf:type b:ChildOfShakespeare. Following similar reasoning, we can also turn this inference around backward; if we instead assert that b:Hamnet rdf:type b:ChildOfShakespeare. b:Judith rdf:type b:ChildOfShakespeare. b:Susanna rdf:type b:ChildOfShakespeare. we can infer that b:Shakespeares_Children foaf:member b:Hamnet. b:Shakespeares_Children foaf:member b:Judith. b:Shakespeares_Children foaf:member b:Susanna. ALTERNATIVE DESCRIPTIONS OF RESTRICTIONS In this book, we describe OWL and its semantics with respect to the interpretation of OWL as RDF triples as defined in the W3C OWL documents. Other characterizations have been used during the history of OWL and even appear in user interfaces of some tools. Each characterization uses its own vocabulary to describe exactly the same things. In this section we review some of the most common