| | I am becoming frustrated with the open-world reasoning in OWL. I have created a list ontology as follows:
<?xml version="1.0"?>
<!DOCTYPE rdf:RDF [
<!ENTITY owl "http://www.w3.org/2002/07/owl#" >
<!ENTITY dc "http://purl.org/dc/elements/1.1/" >
<!ENTITY xsd "http://www.w3.org/2001/XMLSchema#" >
<!ENTITY rdfs "http://www.w3.org/2000/01/rdf-schema#" >
<!ENTITY daml "http://www.daml.org/2001/03/daml+oil#" >
<!ENTITY p1 "http://www.owl-ontologies.com/assert.owl#" >
<!ENTITY rdf "http://www.w3.org/1999/02/22-rdf-syntax-ns#" >
]>
<rdf:RDF xmlns="http://masaka.cs.ohiou.edu/amitchel/util/list.owl#"
xml:base="http://masaka.cs.ohiou.edu/amitchel/util/list.owl"
xmlns:p1="http://www.owl-ontologies.com/assert.owl#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
xmlns:daml="http://www.daml.org/2001/03/daml+oil#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:owl="http://www.w3.org/2002/07/owl#">
<owl:Ontology rdf:about=""/>
<owl:Class rdf:ID="EmptyList">
<owl:equivalentClass>
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Restriction>
<owl:onProperty rdf:resource="#hasContents"/>
<owl:maxCardinality rdf:datatype="&xsd;int">0</owl:maxCardinality>
</owl:Restriction>
<owl:Restriction>
<owl:onProperty rdf:resource="#hasNext"/>
<owl:maxCardinality rdf:datatype="&xsd;int">0</owl:maxCardinality>
</owl:Restriction>
<owl:Class rdf:about="#List"/>
</owl:intersectionOf>
</owl:Class>
</owl:equivalentClass>
<owl:equivalentClass>
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Class rdf:about="#List"/>
<owl:Class>
<owl:complementOf>
<owl:Restriction>
<owl:onProperty rdf:resource="#isFollowedBy"/>
<owl:someValuesFrom rdf:resource="&owl;Thing"/>
</owl:Restriction>
</owl:complementOf>
</owl:Class>
</owl:intersectionOf>
</owl:Class>
</owl:equivalentClass>
</owl:Class>
<owl:ObjectProperty rdf:ID="hasContents">
<rdf:type rdf:resource="&owl;FunctionalProperty"/>
<rdfs:domain rdf:resource="#List"/>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="hasNext">
<rdf:type rdf:resource="&owl;FunctionalProperty"/>
<rdfs:subPropertyOf rdf:resource="#isFollowedBy"/>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="isFollowedBy">
<rdf:type rdf:resource="&owl;TransitiveProperty"/>
<rdfs:domain rdf:resource="#List"/>
<rdfs:range>
<owl:Class>
<owl:unionOf rdf:parseType="Collection">
<owl:Class rdf:about="#List"/>
<owl:Class>
<owl:complementOf rdf:resource="&owl;Thing"/>
</owl:Class>
</owl:unionOf>
</owl:Class>
</rdfs:range>
</owl:ObjectProperty>
<owl:Class rdf:ID="List">
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty rdf:resource="#hasContents"/>
<owl:maxCardinality rdf:datatype="&xsd;int">1</owl:maxCardinality>
</owl:Restriction>
</rdfs:subClassOf>
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty rdf:resource="#hasNext"/>
<owl:maxCardinality rdf:datatype="&xsd;int">1</owl:maxCardinality>
</owl:Restriction>
</rdfs:subClassOf>
<rdfs:subClassOf rdf:resource="&owl;Thing"/>
</owl:Class>
</rdf:RDF>
I have been testing reasoning on the list class using the following Ontology...
<?xml version="1.0"?>
<!DOCTYPE rdf:RDF [
<!ENTITY owl "http://www.w3.org/2002/07/owl#" >
<!ENTITY dc "http://purl.org/dc/elements/1.1/" >
<!ENTITY xsd "http://www.w3.org/2001/XMLSchema#" >
<!ENTITY rdfs "http://www.w3.org/2000/01/rdf-schema#" >
<!ENTITY daml "http://www.daml.org/2001/03/daml+oil#" >
<!ENTITY p2 "http://www.owl-ontologies.com/assert.owl#" >
<!ENTITY rdf "http://www.w3.org/1999/02/22-rdf-syntax-ns#" >
<!ENTITY p1 "http://masaka.cs.ohiou.edu/amitchel/util/list.owl#" >
]>
<rdf:RDF xmlns="http://www.owl-ontologies.com/Ontology1157570502.owl#"
xml:base="http://www.owl-ontologies.com/Ontology1157570502.owl"
xmlns:p1="http://masaka.cs.ohiou.edu/amitchel/util/list.owl#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:p2="http://www.owl-ontologies.com/assert.owl#"
xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
xmlns:daml="http://www.daml.org/2001/03/daml+oil#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:owl="http://www.w3.org/2002/07/owl#">
<owl:Ontology rdf:about="">
<owl:imports rdf:resource="http://masaka.cs.ohiou.edu/amitchel/util/list.owl"/>
</owl:Ontology>
<owl:AllDifferent>
<owl:distinctMembers rdf:parseType="Collection">
<rdf:Description rdf:about="#A"/>
<rdf:Description rdf:about="#B"/>
<rdf:Description rdf:about="#C"/>
<rdf:Description rdf:about="#D"/>
<rdf:Description rdf:about="#E"/>
</owl:distinctMembers>
</owl:AllDifferent>
<owl:AllDifferent>
<owl:distinctMembers rdf:parseType="Collection">
<rdf:Description rdf:about="#one"/>
<rdf:Description rdf:about="#two"/>
<rdf:Description rdf:about="#three"/>
<rdf:Description rdf:about="#four"/>
<rdf:Description rdf:about="#five"/>
<rdf:Description rdf:about="#six"/>
<rdf:Description rdf:about="#seven"/>
<rdf:Description rdf:about="#eight"/>
<rdf:Description rdf:about="#nine"/>
</owl:distinctMembers>
</owl:AllDifferent>
<Character rdf:ID="A"/>
<Character rdf:ID="B"/>
<Character rdf:ID="C"/>
<CharacterItem rdf:ID="Char1">
<p1:hasContents rdf:resource="#A"/>
<p1:hasNext rdf:resource="#Char1"/>
</CharacterItem>
<owl:Class rdf:ID="Character">
<owl:equivalentClass>
<owl:Class>
<owl:oneOf rdf:parseType="Collection">
<rdf:Description rdf:about="#A"/>
<rdf:Description rdf:about="#B"/>
<rdf:Description rdf:about="#C"/>
<rdf:Description rdf:about="#D"/>
<rdf:Description rdf:about="#E"/>
</owl:oneOf>
</owl:Class>
</owl:equivalentClass>
<owl:disjointWith rdf:resource="&p1;List"/>
<owl:disjointWith rdf:resource="#Digit"/>
</owl:Class>
<owl:Class rdf:ID="CharacterItem">
<owl:equivalentClass>
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Restriction>
<owl:onProperty rdf:resource="&p1;hasContents"/>
<owl:allValuesFrom rdf:resource="#Character"/>
</owl:Restriction>
<owl:Class rdf:about="&p1;List"/>
</owl:intersectionOf>
</owl:Class>
</owl:equivalentClass>
</owl:Class>
<owl:Class rdf:ID="CharacterList">
<owl:equivalentClass>
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Class rdf:about="#CharacterItem"/>
<owl:Restriction>
<owl:onProperty rdf:resource="&p1;hasNext"/>
<owl:allValuesFrom rdf:resource="#CharacterItem"/>
</owl:Restriction>
</owl:intersectionOf>
</owl:Class>
</owl:equivalentClass>
</owl:Class>
<owl:Class rdf:ID="CharListReal">
<owl:equivalentClass>
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Class rdf:about="#CharacterItem"/>
<owl:Restriction>
<owl:onProperty rdf:resource="&p1;isFollowedBy"/>
<owl:allValuesFrom rdf:resource="#CharacterItem"/>
</owl:Restriction>
<owl:Restriction>
<owl:onProperty rdf:resource="&p1;isFollowedBy"/>
<owl:someValuesFrom rdf:resource="#CharacterItem"/>
</owl:Restriction>
</owl:intersectionOf>
</owl:Class>
</owl:equivalentClass>
</owl:Class>
<Character rdf:ID="D"/>
<owl:Class rdf:ID="Digit">
<owl:equivalentClass>
<owl:Class>
<owl:oneOf rdf:parseType="Collection">
<rdf:Description rdf:about="#eight"/>
<rdf:Description rdf:about="#five"/>
<rdf:Description rdf:about="#four"/>
<rdf:Description rdf:about="#nine"/>
<rdf:Description rdf:about="#one"/>
<rdf:Description rdf:about="#seven"/>
<rdf:Description rdf:about="#six"/>
<rdf:Description rdf:about="#three"/>
<rdf:Description rdf:about="#two"/>
</owl:oneOf>
</owl:Class>
</owl:equivalentClass>
<owl:disjointWith rdf:resource="&p1;List"/>
<owl:disjointWith rdf:resource="#Character"/>
</owl:Class>
<Character rdf:ID="E"/>
<Digit rdf:ID="eight"/>
<p1:EmptyList rdf:ID="EmptyList"/>
<Digit rdf:ID="five"/>
<Digit rdf:ID="four"/>
<owl:ObjectProperty rdf:ID="hasCharacter">
<rdf:type rdf:resource="&owl;FunctionalProperty"/>
<rdfs:range rdf:resource="#Character"/>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="hasDigit">
<rdf:type rdf:resource="&owl;FunctionalProperty"/>
<rdfs:range rdf:resource="#Digit"/>
</owl:ObjectProperty>
<p1:List rdf:ID="LetterLetterNum">
<p1:hasContents rdf:resource="#B"/>
<p1:hasNext rdf:resource="#LetterNum"/>
</p1:List>
<p1:List rdf:ID="LetterNum">
<p1:hasContents rdf:resource="#C"/>
<p1:hasNext rdf:resource="#Number"/>
</p1:List>
<p1:List rdf:ID="Name">
<p1:hasContents rdf:resource="#A"/>
<p1:hasNext rdf:resource="#EmptyList"/>
</p1:List>
<Digit rdf:ID="nine"/>
<p1:List rdf:ID="Number">
<p1:hasContents rdf:resource="#one"/>
</p1:List>
<owl:Class rdf:ID="NumberItem">
<owl:equivalentClass>
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Restriction>
<owl:onProperty rdf:resource="&p1;hasContents"/>
<owl:allValuesFrom rdf:resource="#Digit"/>
</owl:Restriction>
<owl:Class rdf:about="&p1;List"/>
</owl:intersectionOf>
</owl:Class>
</owl:equivalentClass>
</owl:Class>
<Digit rdf:ID="one"/>
<rdf:Description rdf:about="&p1;List">
<owl:disjointWith rdf:resource="#Character"/>
<owl:disjointWith rdf:resource="#Digit"/>
</rdf:Description>
<p1:List rdf:ID="Reflexive">
<p1:hasContents rdf:resource="#B"/>
<p1:hasNext rdf:resource="#Reflexive"/>
</p1:List>
<Digit rdf:ID="seven"/>
<Digit rdf:ID="six"/>
<Digit rdf:ID="three"/>
<Digit rdf:ID="two"/>
</rdf:RDF>
I am trying to create a CharacterList class that encompases all lists that have only characters in them. I have been attempting to utalize the transitive property isFollowedBy for this purpose. Sadly, since transitive properties can not have cardinality constraints attached to them, I have been unable to force closure of any class on this property. I was hopeful that the restriction: p1:isFollowedBy ∀ CharacterItem would cover it since EmptyList is inferred to be a subclass of CharacterItem and EmptyList is restricted by: ¬(p1:isFollowedBy ∃ owl:Thing). Can anyone out there spot the flaw in my logic? Why is not ¬(p1:isFollowedBy ∃ owl:Thing) [read: EmptyList is never followed by anything = EmptyList is followed by nothing] conceptually the same as placing a maxCardinalityConstraint of zero on p1:isFollowedBy [read: EmptyList can be followed by nothing]?
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| | Posted 9/7/2006 5:51 PM - 45 Views - 2 eProps - 1 Comment
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