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OWL Web Ontology Language
Test Cases
7.1. By Function


Contents


7.1. By Function

7.1.1. owl:AllDifferent

FullPositive Entailment Test:001
Description: (informative) <AllDifferent/Manifest001#test>
using AllDifferent to derive differentFrom
N3 format is informative.
FullPremises: <AllDifferent/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/AllDifferent/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/AllDifferent/premises001" >

    <owl:AllDifferent> 
      <owl:distinctMembers rdf:parseType="Collection">
        <first:Person rdf:about="#Fred" />
        <first:Person rdf:about="#Wilma" />
        <first:Person rdf:about="#Barney" />
        <first:Person rdf:about="#Betty" />
      </owl:distinctMembers>
    </owl:AllDifferent> 

</rdf:RDF>
_:a rdf:type owl:AllDifferent .
first:Fred rdf:type first:Person .
first:Wilma rdf:type first:Person .
first:Barney rdf:type first:Person .
first:Betty rdf:type first:Person .
_:c rdf:first first:Betty .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
_:e rdf:first first:Barney .
_:e rdf:rest _:c .
_:e rdf:type rdf:List .
_:g rdf:first first:Wilma .
_:g rdf:rest _:e .
_:g rdf:type rdf:List .
_:i rdf:first first:Fred .
_:i rdf:rest _:g .
_:i rdf:type rdf:List .
_:a owl:distinctMembers _:i .
FullConclusions: <AllDifferent/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/AllDifferent/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/AllDifferent/conclusions001" >

    <rdf:Description rdf:about="premises001#Barney">
        <owl:differentFrom rdf:resource="premises001#Fred"/>
    </rdf:Description>

</rdf:RDF>
first:Barney owl:differentFrom first:Fred .

7.1.2. owl:FunctionalProperty

FullPositive Entailment Test:001
Description: (informative) <FunctionalProperty/Manifest001#test>
If prop belongs to owl:FunctionalProperty, and subject denotes a resource which is the subject of two prop triples, then the objects of these triples have the same denotation.
N3 format is informative.
FullPremises: <FunctionalProperty/premises001>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xmlns:first="http://www.w3.org/2002/03owlt/FunctionalProperty/premises001#" 
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/premises001" >
    <owl:FunctionalProperty rdf:ID="prop"/>
    <rdf:Description rdf:ID="subject">
      <first:prop rdf:resource="#object1" />
      <first:prop rdf:resource="#object2" />
    </rdf:Description>
</rdf:RDF>
first:prop rdf:type owl:FunctionalProperty .
first:subject first:prop first:object1 .
first:subject first:prop first:object2 .
FullConclusions: <FunctionalProperty/conclusions001>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/conclusions001" >
    <rdf:Description rdf:about="premises001#object1">
      <owl:sameIndividualAs rdf:resource="premises001#object2" />
    </rdf:Description>
</rdf:RDF>
first:object1 owl:sameIndividualAs first:object2 .

FullPositive Entailment Test:002
Description: (informative) <FunctionalProperty/Manifest002#test>
If prop belongs to owl:FunctionalProperty, and subject denotes a resource which is the subject of two prop triples, then the objects of these triples have the same denotation.Hence any assertion made using one of them can be transferred to the other.
N3 format is informative.
Namespaces:
@prefix eg: <http://www.example.org/> .
FullPremises: <FunctionalProperty/premises002>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xmlns:eg ="http://www.example.org/"
  xmlns:first="http://www.w3.org/2002/03owlt/FunctionalProperty/premises002#" 
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/premises002" >
    <owl:FunctionalProperty rdf:ID="prop"/>
    <rdf:Description rdf:ID="subject">
      <first:prop>
          <rdf:Description rdf:ID="object1">
            <eg:prop2>value</eg:prop2>
          </rdf:Description>
      </first:prop>
      <first:prop rdf:resource="#object2" />
    </rdf:Description>
</rdf:RDF>
first:prop rdf:type owl:FunctionalProperty .
first:object1 eg:prop2 "value" .
first:subject first:prop first:object1 .
first:subject first:prop first:object2 .
FullConclusions: <FunctionalProperty/conclusions002>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:eg ="http://www.example.org/"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/conclusions002" >
    <rdf:Description rdf:about="premises002#object2" >
        <eg:prop2>value</eg:prop2>
    </rdf:Description>
</rdf:RDF>
first:object2 eg:prop2 "value" .

FullPositive Entailment Test:003
Description: (informative) <FunctionalProperty/Manifest003#test>
If prop is an owl:FunctionalProperty, then its inverse is an owl:InverseFunctionalProperty.
N3 format is informative.
FullPremises: <FunctionalProperty/premises003>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/premises003" >
    <owl:FunctionalProperty rdf:ID="prop">
      <owl:inverseOf rdf:resource="#inv"/>
    </owl:FunctionalProperty>
</rdf:RDF>
first:prop rdf:type owl:FunctionalProperty .
first:prop owl:inverseOf first:inv .
LiteConclusions: <FunctionalProperty/conclusions003>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/conclusions003" >
    <owl:InverseFunctionalProperty rdf:about="premises003#inv"/>
</rdf:RDF>
first:inv rdf:type owl:InverseFunctionalProperty .

FullPositive Entailment Test:004
Description: (informative) <FunctionalProperty/Manifest004#test>
If the range of prop is a singleton set then it is necessarily functional, (i.e. every member of its domain has a single value) and so it is an owl:FunctionalProperty.
N3 format is informative.
FullPremises: <FunctionalProperty/premises004>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"  
  xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/premises004" >
    <owl:ObjectProperty rdf:ID="prop">
      <rdfs:range rdf:resource="#Singleton"/>
    </owl:ObjectProperty>
    <rdfs:Class rdf:ID="Singleton">
      <owl:oneOf rdf:parseType="Collection">
          <rdf:Description/>
      </owl:oneOf>
    </rdfs:Class>
</rdf:RDF>
first:prop rdf:type owl:ObjectProperty .
first:prop rdfs:range first:Singleton .
first:Singleton rdf:type rdfs:Class .
_:a rdf:first _:b .
_:a rdf:rest rdf:nil .
_:a rdf:type rdf:List .
first:Singleton owl:oneOf _:a .
FullConclusions: <FunctionalProperty/conclusions004>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/conclusions004" >
    <owl:FunctionalProperty rdf:about="premises004#prop"/>
</rdf:RDF>
first:prop rdf:type owl:FunctionalProperty .

7.1.3. owl:InverseFunctionalProperty

FullPositive Entailment Test:001
Description: (informative) <InverseFunctionalProperty/Manifest001#test>
If prop belongs to owl:InverseFunctionalProperty, and object denotes a resource which is the object of two prop triples, then the subjects of these triples have the same denotation.
N3 format is informative.
FullPremises: <InverseFunctionalProperty/premises001>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xmlns:first="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises001#" 
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises001" >
    <owl:InverseFunctionalProperty rdf:ID="prop"/>
    <rdf:Description rdf:ID="subject1">
      <first:prop rdf:resource="#object" />
    </rdf:Description>
    <rdf:Description rdf:ID="subject2">
      <first:prop rdf:resource="#object" />
    </rdf:Description>
</rdf:RDF>
first:prop rdf:type owl:InverseFunctionalProperty .
first:subject1 first:prop first:object .
first:subject2 first:prop first:object .
FullConclusions: <InverseFunctionalProperty/conclusions001>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/conclusions001" >
    <rdf:Description rdf:about="premises001#subject1">
      <owl:sameIndividualAs rdf:resource="premises001#subject2" />
    </rdf:Description>
</rdf:RDF>
first:subject1 owl:sameIndividualAs first:subject2 .

FullPositive Entailment Test:002
Description: (informative) <InverseFunctionalProperty/Manifest002#test>
If prop belongs to owl:InverseFunctionalProperty, and object denotes a resource which is the object of two prop triples, then the subjects of these triples have the same denotation. Hence any assertion made using one of them can be transferred to the other.
N3 format is informative.
Namespaces:
@prefix eg: <http://www.example.org/> .
FullPremises: <InverseFunctionalProperty/premises002>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xmlns:eg ="http://www.example.org/"
  xmlns:first="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises002#" 
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises002" >
    <owl:InverseFunctionalProperty rdf:ID="prop"/>
    <rdf:Description rdf:ID="subject1" >
      <first:prop rdf:resource="#object" />
      <eg:prop2>value</eg:prop2>
    </rdf:Description>
    <rdf:Description rdf:ID="subject2" >
      <first:prop rdf:resource="#object" />
    </rdf:Description>
</rdf:RDF>
first:prop rdf:type owl:InverseFunctionalProperty .
first:subject1 first:prop first:object .
first:subject1 eg:prop2 "value" .
first:subject2 first:prop first:object .
FullConclusions: <InverseFunctionalProperty/conclusions002>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:eg ="http://www.example.org/"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/conclusions002" >
    <rdf:Description rdf:about="premises002#subject2" >
      <eg:prop2>value</eg:prop2>
    </rdf:Description>
</rdf:RDF>
first:subject2 eg:prop2 "value" .

FullPositive Entailment Test:003
Description: (informative) <InverseFunctionalProperty/Manifest003#test>
If prop is an owl:InverseFunctionalProperty, then its inverse is an owl:FunctionalProperty.
N3 format is informative.
FullPremises: <InverseFunctionalProperty/premises003>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises003" >
    <owl:InverseFunctionalProperty rdf:ID="prop">
      <owl:inverseOf rdf:resource="#inv"/>
    </owl:InverseFunctionalProperty>
</rdf:RDF>
first:prop rdf:type owl:InverseFunctionalProperty .
first:prop owl:inverseOf first:inv .
FullConclusions: <InverseFunctionalProperty/conclusions003>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/conclusions003" >
    <owl:FunctionalProperty rdf:about="premises003#inv"/>
</rdf:RDF>
first:inv rdf:type owl:FunctionalProperty .

FullPositive Entailment Test:004
Description: (informative) <InverseFunctionalProperty/Manifest004#test>
If the domain of prop is a singleton set then it is necessarily inverse functional, (i.e. every member of its range is the value of a single item) so it is an owl:InverseFunctionalProperty.
N3 format is informative.
FullPremises: <InverseFunctionalProperty/premises004>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"  
  xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises004" >
    <owl:ObjectProperty rdf:ID="prop">
      <rdfs:domain rdf:resource="#Singleton"/>
    </owl:ObjectProperty>
    <rdfs:Class rdf:ID="Singleton">
      <owl:oneOf rdf:parseType="Collection">
          <rdf:Description/>
      </owl:oneOf>
    </rdfs:Class>
</rdf:RDF>
first:prop rdf:type owl:ObjectProperty .
first:prop rdfs:domain first:Singleton .
first:Singleton rdf:type rdfs:Class .
_:a rdf:first _:b .
_:a rdf:rest rdf:nil .
_:a rdf:type rdf:List .
first:Singleton owl:oneOf _:a .
LiteConclusions: <InverseFunctionalProperty/conclusions004>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/conclusions004" >
    <owl:InverseFunctionalProperty rdf:about="premises004#prop"/>
</rdf:RDF>
first:prop rdf:type owl:InverseFunctionalProperty .

7.1.4. owl:Nothing

DLOWL described in OWL.002
Description: (informative) <Nothing/Manifest002#test>
An empty owl:Class has the same class extension as owl:Nothing.
N3 format is informative.
DLTrue: <Nothing/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xml:base='http://www.w3.org/2002/03owlt/Nothing/conclusions002'
    xmlns:owl="http://www.w3.org/2002/07/owl#">

   <owl:Class>
      <owl:oneOf rdf:parseType="Collection"/>
      <owl:equivalentClass  rdf:resource="http://www.w3.org/2002/07/owl#Nothing" />
   </owl:Class>

</rdf:RDF>
_:a rdf:type owl:Class .
_:a owl:oneOf rdf:nil .
_:a owl:equivalentClass owl:Nothing .

7.1.5. owl:SymmetricProperty

FullPositive Entailment Test:001
Description: (informative) <SymmetricProperty/Manifest001#test>
A simple illustration of symmetric properties.
N3 format is informative.
FullPremises: <SymmetricProperty/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/SymmetricProperty/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/SymmetricProperty/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/SymmetricProperty/premises001" >

    <rdf:Description rdf:about="premises001#Ghent">
        <first:path rdf:resource="premises001#Antwerp"/>
    </rdf:Description>

    <owl:SymmetricProperty rdf:about="premises001#path"/>

</rdf:RDF>
first:Ghent first:path first:Antwerp .
first:path rdf:type owl:SymmetricProperty .
FullConclusions: <SymmetricProperty/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/SymmetricProperty/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/SymmetricProperty/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/SymmetricProperty/conclusions001" >

    <rdf:Description rdf:about="premises001#Antwerp">
        <first:path rdf:resource="premises001#Ghent"/>
    </rdf:Description>

</rdf:RDF>
first:Antwerp first:path first:Ghent .

7.1.6. owl:TransitiveProperty

FullPositive Entailment Test:001
Description: (informative) <TransitiveProperty/Manifest001#test>
A simple illustration of transitivity.
N3 format is informative.
FullPremises: <TransitiveProperty/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/TransitiveProperty/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/TransitiveProperty/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/TransitiveProperty/premises001" >

    <rdf:Description rdf:about="premises001#Antwerp">
        <first:path rdf:resource="premises001#Amsterdam"/>
    </rdf:Description>

    <rdf:Description rdf:about="premises001#Ghent">
        <first:path rdf:resource="premises001#Antwerp"/>
    </rdf:Description>

    <owl:TransitiveProperty rdf:about="premises001#path"/>

</rdf:RDF>
first:Antwerp first:path first:Amsterdam .
first:Ghent first:path first:Antwerp .
first:path rdf:type owl:TransitiveProperty .
FullConclusions: <TransitiveProperty/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/TransitiveProperty/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/TransitiveProperty/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/TransitiveProperty/conclusions001" >

    <rdf:Description rdf:about="premises001#Ghent">
        <first:path rdf:resource="premises001#Amsterdam"/>
    </rdf:Description>

</rdf:RDF>
first:Ghent first:path first:Amsterdam .

7.1.7. owl:allValuesFrom

LitePositive Entailment Test:001
Description: (informative) <allValuesFrom/Manifest001#test>
A simple example.
N3 format is informative.
LitePremises: <allValuesFrom/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/allValuesFrom/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/allValuesFrom/premises001" >
    <owl:Class rdf:ID="r">
      <rdfs:subClassOf>
        <owl:Restriction>
            <owl:onProperty rdf:resource="#p"/>
            <owl:allValuesFrom rdf:resource="#c"/>
        </owl:Restriction>
      </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:ID="p"/>
    <owl:Class rdf:ID="c"/>
    <first:r rdf:ID="i">
       <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing"/>
       <first:p>
         <owl:Thing rdf:ID="o" />
       </first:p>
    </first:r>
</rdf:RDF>
first:r rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:allValuesFrom first:c .
first:r rdfs:subClassOf _:a .
first:p rdf:type owl:ObjectProperty .
first:c rdf:type owl:Class .
first:i rdf:type first:r .
first:i rdf:type owl:Thing .
first:o rdf:type owl:Thing .
first:i first:p first:o .
LiteConclusions: <allValuesFrom/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:first="http://www.w3.org/2002/03owlt/allValuesFrom/premises001#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/allValuesFrom/conclusions001" >
    <first:c rdf:about="premises001#o">
       <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing"/>
    </first:c>
    <owl:Class rdf:about="premises001#c"/>
</rdf:RDF>
first:o rdf:type first:c .
first:o rdf:type owl:Thing .
first:c rdf:type owl:Class .

LiteNegative Entailment Test:002
Description: (informative) <allValuesFrom/Manifest002#test>
Another simple example; contrast with owl:someValuesFrom.
N3 format is informative.
LitePremises: <allValuesFrom/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/allValuesFrom/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/allValuesFrom/premises002" >
    <owl:Class rdf:ID="r">
      <rdfs:subClassOf>
        <owl:Restriction>
            <owl:onProperty rdf:resource="#p"/>
            <owl:allValuesFrom rdf:resource="#c"/>
        </owl:Restriction>
      </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:ID="p"/>

    <owl:Class rdf:ID="c"/>
    <first:r rdf:ID="i">
      <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing"/>
    </first:r>
</rdf:RDF>
first:r rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:allValuesFrom first:c .
first:r rdfs:subClassOf _:a .
first:p rdf:type owl:ObjectProperty .
first:c rdf:type owl:Class .
first:i rdf:type first:r .
first:i rdf:type owl:Thing .
LiteConclusions: <allValuesFrom/nonconclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/allValuesFrom/premises002#"
    xmlns:second="http://www.w3.org/2002/03owlt/allValuesFrom/nonconclusions002#"
    xml:base="http://www.w3.org/2002/03owlt/allValuesFrom/nonconclusions002" >
    <owl:Thing rdf:about="premises002#i">
        <first:p>
           <first:c rdf:nodeID="o" />
         </first:p>
    </owl:Thing>
    <owl:Thing rdf:nodeID="o" />
    <owl:ObjectProperty rdf:about="premises002#p"/>
    <owl:Class rdf:about="premises002#c"/>
</rdf:RDF>
first:i rdf:type owl:Thing .
_:a rdf:type first:c .
first:i first:p _:a .
_:a rdf:type owl:Thing .
first:p rdf:type owl:ObjectProperty .
first:c rdf:type owl:Class .

7.1.8. owl:cardinality

LitePositive Entailment Test:001
Description: (informative) <cardinality/Manifest001#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
LitePremises: <cardinality/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises001" >
    <owl:Class rdf:ID="c">
      <rdfs:subClassOf>
         <owl:Restriction>
            <owl:onProperty rdf:resource="#p"/>
            <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
            >1</owl:cardinality>
         </owl:Restriction>
      </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
first:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:cardinality "1"^^xsd:nonNegativeInteger  .
first:c rdfs:subClassOf _:a .
first:p rdf:type owl:ObjectProperty .
LiteConclusions: <cardinality/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions001" >
    <owl:Class rdf:about="premises001#c">
      <rdfs:subClassOf>
        <owl:Restriction>
          <owl:onProperty rdf:resource="premises001#p"/>
          <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
          >1</owl:maxCardinality>
        </owl:Restriction>
      </rdfs:subClassOf>
      <rdfs:subClassOf>
        <owl:Restriction>
          <owl:onProperty rdf:resource="premises001#p"/>
          <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
           >1</owl:minCardinality>
         </owl:Restriction>
       </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:about="premises001#p"/>
</rdf:RDF>
first:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:maxCardinality "1"^^xsd:nonNegativeInteger  .
first:c rdfs:subClassOf _:a .
_:c rdf:type owl:Restriction .
_:c owl:onProperty first:p .
_:c owl:minCardinality "1"^^xsd:nonNegativeInteger  .
first:c rdfs:subClassOf _:c .
first:p rdf:type owl:ObjectProperty .

LitePositive Entailment Test:002
Description: (informative) <cardinality/Manifest002#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
LitePremises: <cardinality/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises002" >    
    <owl:Class rdf:about="conclusions002#c">
      <rdfs:subClassOf>
        <owl:Restriction>
          <owl:onProperty rdf:resource="conclusions002#p"/>
          <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
          >1</owl:maxCardinality>
        </owl:Restriction>
      </rdfs:subClassOf>
      <rdfs:subClassOf>
        <owl:Restriction>
          <owl:onProperty rdf:resource="conclusions002#p"/>
          <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
          >1</owl:minCardinality>
        </owl:Restriction>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:about="conclusions002#p"/>
</rdf:RDF>
second:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty second:p .
_:a owl:maxCardinality "1"^^xsd:nonNegativeInteger  .
second:c rdfs:subClassOf _:a .
_:c rdf:type owl:Restriction .
_:c owl:onProperty second:p .
_:c owl:minCardinality "1"^^xsd:nonNegativeInteger  .
second:c rdfs:subClassOf _:c .
second:p rdf:type owl:ObjectProperty .
LiteConclusions: <cardinality/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions002" >
    <owl:Class rdf:ID="c">
      <rdfs:subClassOf>
        <owl:Restriction>
          <owl:onProperty rdf:resource="#p"/>
          <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
          >1</owl:cardinality>
        </owl:Restriction>
      </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
second:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty second:p .
_:a owl:cardinality "1"^^xsd:nonNegativeInteger  .
second:c rdfs:subClassOf _:a .
second:p rdf:type owl:ObjectProperty .

DLPositive Entailment Test:003
Description: (informative) <cardinality/Manifest003#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
DLPremises: <cardinality/premises003>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises003" >
    <owl:Class rdf:ID="c">
      <rdfs:subClassOf>
        <owl:Restriction>
          <owl:onProperty rdf:resource="#p"/>
          <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
          >2</owl:cardinality>
        </owl:Restriction>
      </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
first:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:cardinality "2"^^xsd:nonNegativeInteger  .
first:c rdfs:subClassOf _:a .
first:p rdf:type owl:ObjectProperty .
DLConclusions: <cardinality/conclusions003>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions003" >
    <owl:Class rdf:about="premises003#c">
      <rdfs:subClassOf>
        <owl:Restriction>
          <owl:onProperty rdf:resource="premises003#p"/>
          <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
          >2</owl:maxCardinality>
        </owl:Restriction>
      </rdfs:subClassOf>
      <rdfs:subClassOf>
        <owl:Restriction>
          <owl:onProperty rdf:resource="premises003#p"/>
          <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
          >2</owl:minCardinality>
        </owl:Restriction>
      </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:about="premises003#p"/>
</rdf:RDF>
first:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:maxCardinality "2"^^xsd:nonNegativeInteger  .
first:c rdfs:subClassOf _:a .
_:c rdf:type owl:Restriction .
_:c owl:onProperty first:p .
_:c owl:minCardinality "2"^^xsd:nonNegativeInteger  .
first:c rdfs:subClassOf _:c .
first:p rdf:type owl:ObjectProperty .

DLPositive Entailment Test:004
Description: (informative) <cardinality/Manifest004#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
DLPremises: <cardinality/premises004>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises004" >    
    <owl:Class rdf:about="conclusions004#c">
      <rdfs:subClassOf>
          <owl:Class>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="conclusions004#p"/>
                   <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:maxCardinality>
                </owl:Restriction>
                <owl:Restriction>
                   <owl:onProperty rdf:resource="conclusions004#p"/>
                   <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:minCardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </owl:Class>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:about="conclusions004#p"/>
</rdf:RDF>
second:c rdf:type owl:Class .
_:a rdf:type owl:Class .
_:c rdf:type owl:Restriction .
_:c owl:onProperty second:p .
_:c owl:maxCardinality "2"^^xsd:nonNegativeInteger  .
_:e rdf:type owl:Restriction .
_:e owl:onProperty second:p .
_:e owl:minCardinality "2"^^xsd:nonNegativeInteger  .
_:g rdf:first _:e .
_:g rdf:rest rdf:nil .
_:g rdf:type rdf:List .
_:i rdf:first _:c .
_:i rdf:rest _:g .
_:i rdf:type rdf:List .
_:a owl:intersectionOf _:i .
second:c rdfs:subClassOf _:a .
second:p rdf:type owl:ObjectProperty .
DLConclusions: <cardinality/conclusions004>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions004" >
    <owl:Class rdf:ID="c">
      <rdfs:subClassOf>
          <owl:Class>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:cardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </owl:Class>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
second:c rdf:type owl:Class .
_:a rdf:type owl:Class .
_:c rdf:type owl:Restriction .
_:c owl:onProperty second:p .
_:c owl:cardinality "2"^^xsd:nonNegativeInteger  .
_:e rdf:first _:c .
_:e rdf:rest rdf:nil .
_:e rdf:type rdf:List .
_:a owl:intersectionOf _:e .
second:c rdfs:subClassOf _:a .
second:p rdf:type owl:ObjectProperty .

7.1.9. owl:complementOf

FullPositive Entailment Test:001
Description: (informative) <complementOf/Manifest001#test>
complementOf is a SymmetricProperty.
N3 format is informative.
FullPremises: <complementOf/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/complementOf/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/complementOf/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/complementOf/premises001" >

    <rdf:Description rdf:about="premises001#A">
        <owl:complementOf rdf:resource="premises001#B"/>
    </rdf:Description>

</rdf:RDF>
first:A owl:complementOf first:B .
FullConclusions: <complementOf/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/complementOf/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/complementOf/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/complementOf/conclusions001" >

    <rdf:Description rdf:about="premises001#B">
        <owl:complementOf rdf:resource="premises001#A"/>
    </rdf:Description>

</rdf:RDF>
first:B owl:complementOf first:A .

7.1.10. owl:differentFrom

FullPositive Entailment Test:001
Description: (informative) <differentFrom/Manifest001#test>
differentFrom is a SymmetricProperty.
N3 format is informative.
FullPremises: <differentFrom/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/differentFrom/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/differentFrom/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/differentFrom/premises001" >

    <rdf:Description rdf:about="premises001#a">
        <owl:differentFrom rdf:resource="premises001#b"/>
    </rdf:Description>

</rdf:RDF>
first:a owl:differentFrom first:b .
FullConclusions: <differentFrom/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/differentFrom/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/differentFrom/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/differentFrom/conclusions001" >

    <rdf:Description rdf:about="premises001#b">
        <owl:differentFrom rdf:resource="premises001#a"/>
    </rdf:Description>

</rdf:RDF>
first:b owl:differentFrom first:a .

FullPositive Entailment Test:002
Description: (informative) <differentFrom/Manifest002#test>
using distinctMembers to derive differentFrom
N3 format is informative.
FullPremises: <differentFrom/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/differentFrom/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/differentFrom/premises002" >

    <owl:AllDifferent> 
      <owl:distinctMembers rdf:parseType="Collection">
        <first:Person rdf:about="#Fred" />
        <first:Person rdf:about="#Wilma" />
        <first:Person rdf:about="#Barney" />
        <first:Person rdf:about="#Betty" />
      </owl:distinctMembers>
    </owl:AllDifferent> 

</rdf:RDF>
_:a rdf:type owl:AllDifferent .
first:Fred rdf:type first:Person .
first:Wilma rdf:type first:Person .
first:Barney rdf:type first:Person .
first:Betty rdf:type first:Person .
_:c rdf:first first:Betty .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
_:e rdf:first first:Barney .
_:e rdf:rest _:c .
_:e rdf:type rdf:List .
_:g rdf:first first:Wilma .
_:g rdf:rest _:e .
_:g rdf:type rdf:List .
_:i rdf:first first:Fred .
_:i rdf:rest _:g .
_:i rdf:type rdf:List .
_:a owl:distinctMembers _:i .
FullConclusions: <differentFrom/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/differentFrom/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/differentFrom/conclusions002" >

    <rdf:Description rdf:about="premises002#Barney">
        <owl:differentFrom rdf:resource="premises002#Wilma"/>
    </rdf:Description>

</rdf:RDF>
first:Barney owl:differentFrom first:Wilma .

7.1.11. owl:disjointWith

DLPositive Entailment Test:001
Description: (informative) <disjointWith/Manifest001#test>
Disjoint classes have different members.
N3 format is informative.
DLPremises: <disjointWith/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:first="http://www.w3.org/2002/03owlt/disjointWith/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/disjointWith/premises001" >
   <owl:Class rdf:ID="A">
      <owl:disjointWith>
           <owl:Class rdf:ID="B"/>
      </owl:disjointWith>
   </owl:Class>
   <first:A rdf:ID="a"/>
   <owl:Thing rdf:about="#a"/>
   <first:B rdf:ID="b"/>
   <owl:Thing rdf:about="#b"/>
</rdf:RDF>
first:A rdf:type owl:Class .
first:B rdf:type owl:Class .
first:A owl:disjointWith first:B .
first:a rdf:type first:A .
first:a rdf:type owl:Thing .
first:b rdf:type first:B .
first:b rdf:type owl:Thing .
LiteConclusions: <disjointWith/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/disjointWith/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/disjointWith/conclusions001" >
    <owl:Thing rdf:about="premises001#a">
       <owl:differentFrom>
          <owl:Thing rdf:about="premises001#b"/>
       </owl:differentFrom>
    </owl:Thing>
</rdf:RDF>
first:a rdf:type owl:Thing .
first:b rdf:type owl:Thing .
first:a owl:differentFrom first:b .

FullPositive Entailment Test:002
Description: (informative) <disjointWith/Manifest002#test>
Disjoint classes have different members.
N3 format is informative.
FullPremises: <disjointWith/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/disjointWith/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/disjointWith/premises002" >

   <rdf:Description rdf:ID="A">
      <owl:disjointWith>
           <rdf:Description rdf:ID="B"/>
      </owl:disjointWith>
   </rdf:Description>
   <first:A rdf:ID="a"/>
   <first:B rdf:ID="b"/>

</rdf:RDF>
first:A owl:disjointWith first:B .
first:a rdf:type first:A .
first:b rdf:type first:B .
FullConclusions: <disjointWith/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/disjointWith/conclusions002" >
    <rdf:Description rdf:about="premises002#a">
       <owl:differentFrom rdf:resource="premises002#b"/>
    </rdf:Description>
</rdf:RDF>
first:a owl:differentFrom first:b .

7.1.12. owl:distinctMembers

FullPositive Entailment Test:001
Description: (informative) <distinctMembers/Manifest001#test>
using distinctMembers to derive differentFrom
N3 format is informative.
FullPremises: <distinctMembers/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/distinctMembers/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/distinctMembers/premises001" >

    <owl:AllDifferent> 
      <owl:distinctMembers rdf:parseType="Collection">
        <first:Person rdf:about="#Fred" />
        <first:Person rdf:about="#Wilma" />
        <first:Person rdf:about="#Barney" />
        <first:Person rdf:about="#Betty" />
      </owl:distinctMembers>
    </owl:AllDifferent> 

</rdf:RDF>
_:a rdf:type owl:AllDifferent .
first:Fred rdf:type first:Person .
first:Wilma rdf:type first:Person .
first:Barney rdf:type first:Person .
first:Betty rdf:type first:Person .
_:c rdf:first first:Betty .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
_:e rdf:first first:Barney .
_:e rdf:rest _:c .
_:e rdf:type rdf:List .
_:g rdf:first first:Wilma .
_:g rdf:rest _:e .
_:g rdf:type rdf:List .
_:i rdf:first first:Fred .
_:i rdf:rest _:g .
_:i rdf:type rdf:List .
_:a owl:distinctMembers _:i .
FullConclusions: <distinctMembers/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/distinctMembers/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/distinctMembers/conclusions001" >

    <rdf:Description rdf:about="premises001#Fred">
        <owl:differentFrom rdf:resource="premises001#Barney"/>
    </rdf:Description>

</rdf:RDF>
first:Fred owl:differentFrom first:Barney .

7.1.13. owl:equivalentClass

LitePositive Entailment Test:001
Description: (informative) <equivalentClass/Manifest001#test>
Two classes may have the same class extension.
N3 format is informative.
LitePremises: <equivalentClass/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/equivalentClass/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/premises001" >
   <owl:Class rdf:ID="Car">
     <owl:equivalentClass>
       <owl:Class rdf:ID="Automobile"/>
     </owl:equivalentClass>
  </owl:Class>
  <first:Car rdf:ID="car">
     <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing" />
  </first:Car>
  <first:Automobile rdf:ID="auto">
     <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing" />
  </first:Automobile>
</rdf:RDF>
first:Car rdf:type owl:Class .
first:Automobile rdf:type owl:Class .
first:Car owl:equivalentClass first:Automobile .
first:car rdf:type first:Car .
first:car rdf:type owl:Thing .
first:auto rdf:type first:Automobile .
first:auto rdf:type owl:Thing .
LiteConclusions: <equivalentClass/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/equivalentClass/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/conclusions001" >
  <first:Car rdf:about="premises001#auto">
     <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing" />
  </first:Car>
  <first:Automobile rdf:about="premises001#car">
     <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing" />
  </first:Automobile>
   <owl:Class rdf:about="premises001#Car"/>
   <owl:Class rdf:about="premises001#Automobile"/>
</rdf:RDF>
first:auto rdf:type first:Car .
first:auto rdf:type owl:Thing .
first:car rdf:type first:Automobile .
first:car rdf:type owl:Thing .
first:Car rdf:type owl:Class .
first:Automobile rdf:type owl:Class .

LitePositive Entailment Test:002
Description: (informative) <equivalentClass/Manifest002#test>
Two classes may be different names for the same set of individuals
N3 format is informative.
LitePremises: <equivalentClass/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/premises002" >
   <owl:Class rdf:ID="Car">
     <owl:equivalentClass>
       <owl:Class rdf:ID="Automobile"/>
     </owl:equivalentClass>
  </owl:Class>
</rdf:RDF>
first:Car rdf:type owl:Class .
first:Automobile rdf:type owl:Class .
first:Car owl:equivalentClass first:Automobile .
LiteConclusions: <equivalentClass/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/conclusions002" >
   <owl:Class rdf:about="premises002#Car">
     <rdfs:subClassOf>
       <owl:Class rdf:about="premises002#Automobile">
          <rdfs:subClassOf rdf:resource="premises002#Car" />
       </owl:Class>
     </rdfs:subClassOf>
  </owl:Class>
</rdf:RDF>
first:Car rdf:type owl:Class .
first:Automobile rdf:type owl:Class .
first:Automobile rdfs:subClassOf first:Car .
first:Car rdfs:subClassOf first:Automobile .

LitePositive Entailment Test:003
Description: (informative) <equivalentClass/Manifest003#test>
Two classes may be different names for the same set of individuals
N3 format is informative.
LitePremises: <equivalentClass/premises003>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/premises003" >
   <owl:Class rdf:about="conclusions003#Car">
     <rdfs:subClassOf>
       <owl:Class rdf:about="conclusions003#Automobile">
          <rdfs:subClassOf rdf:resource="conclusions003#Car" />
       </owl:Class>
     </rdfs:subClassOf>
  </owl:Class>
</rdf:RDF>
second:Car rdf:type owl:Class .
second:Automobile rdf:type owl:Class .
second:Automobile rdfs:subClassOf second:Car .
second:Car rdfs:subClassOf second:Automobile .
LiteConclusions: <equivalentClass/conclusions003>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/conclusions003" >
   <owl:Class rdf:ID="Car">
     <owl:equivalentClass>
       <owl:Class rdf:ID="Automobile"/>
     </owl:equivalentClass>
  </owl:Class>
</rdf:RDF>
second:Car rdf:type owl:Class .
second:Automobile rdf:type owl:Class .
second:Car owl:equivalentClass second:Automobile .

LitePositive Entailment Test:004
Description: (informative) <equivalentClass/Manifest004#test>
Two classes with the same complete description are equivalent.
N3 format is informative.
LitePremises: <equivalentClass/premises004>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/premises004" >
    <owl:Class rdf:ID="c1">
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:cardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </owl:Class>
    <owl:Class rdf:ID="c2">
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:cardinality>
                </owl:Restriction>
              </owl:intersectionOf>
     </owl:Class>
     <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
first:c1 rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:cardinality "1"^^xsd:nonNegativeInteger  .
_:c rdf:first _:a .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
first:c1 owl:intersectionOf _:c .
first:c2 rdf:type owl:Class .
_:e rdf:type owl:Restriction .
_:e owl:onProperty first:p .
_:e owl:cardinality "1"^^xsd:nonNegativeInteger  .
_:g rdf:first _:e .
_:g rdf:rest rdf:nil .
_:g rdf:type rdf:List .
first:c2 owl:intersectionOf _:g .
first:p rdf:type owl:ObjectProperty .
LiteConclusions: <equivalentClass/conclusions004>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/conclusions004" >
<owl:Class rdf:about="premises004#c1">
     <owl:equivalentClass>
       <owl:Class rdf:about="premises004#c2"/>
     </owl:equivalentClass>
  </owl:Class>
</rdf:RDF>
first:c1 rdf:type owl:Class .
first:c2 rdf:type owl:Class .
first:c1 owl:equivalentClass first:c2 .

LiteNegative Entailment Test:005
Description: (informative) <equivalentClass/Manifest005#test>
Two classes with the same partial description are not equivalent.
N3 format is informative.
LitePremises: <equivalentClass/premises005>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/premises005" >
    <owl:Class rdf:ID="c1">
      <rdfs:subClassOf>
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:cardinality>
                </owl:Restriction>
       </rdfs:subClassOf>
     </owl:Class>
    <owl:Class rdf:ID="c2">
      <rdfs:subClassOf>
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:cardinality>
                </owl:Restriction>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
first:c1 rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:cardinality "1"^^xsd:nonNegativeInteger  .
first:c1 rdfs:subClassOf _:a .
first:c2 rdf:type owl:Class .
_:c rdf:type owl:Restriction .
_:c owl:onProperty first:p .
_:c owl:cardinality "1"^^xsd:nonNegativeInteger  .
first:c2 rdfs:subClassOf _:c .
first:p rdf:type owl:ObjectProperty .
LiteConclusions: <equivalentClass/nonconclusions005>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/nonconclusions005" >
<owl:Class rdf:about="premises005#c1">
     <owl:equivalentClass>
       <owl:Class rdf:about="premises005#c2"/>
     </owl:equivalentClass>
  </owl:Class>
</rdf:RDF>
first:c1 rdf:type owl:Class .
first:c2 rdf:type owl:Class .
first:c1 owl:equivalentClass first:c2 .

DLPositive Entailment Test:006
Description: (informative) <equivalentClass/Manifest006#test>
De Morgan's law.
N3 format is informative.
LitePremises: <equivalentClass/premises006>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/premises006" >
   <owl:Class rdf:ID="A"/>
   <owl:Class rdf:ID="B"/>
</rdf:RDF>
first:A rdf:type owl:Class .
first:B rdf:type owl:Class .
DLConclusions: <equivalentClass/conclusions006>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentClass/conclusions006" >
   <owl:Class>
      <owl:intersectionOf rdf:parseType="Collection">
          <owl:Class>
             <owl:complementOf rdf:resource="premises006#A"/>
          </owl:Class>
          <owl:Class>
             <owl:complementOf rdf:resource="premises006#B"/>
          </owl:Class>
      </owl:intersectionOf>
      <owl:equivalentClass>
        <owl:Class>
          <owl:complementOf>
             <owl:Class>
               <owl:unionOf rdf:parseType="Collection">
                 <rdf:Description rdf:about="premises006#A"/>
                 <rdf:Description rdf:about="premises006#B"/>
               </owl:unionOf>
             </owl:Class>
          </owl:complementOf>
        </owl:Class>
      </owl:equivalentClass>
   </owl:Class>   
   <owl:Class rdf:about="premises006#A"/>
   <owl:Class rdf:about="premises006#B"/>
</rdf:RDF>
_:a rdf:type owl:Class .
_:c rdf:type owl:Class .
_:c owl:complementOf first:A .
_:e rdf:type owl:Class .
_:e owl:complementOf first:B .
_:g rdf:first _:e .
_:g rdf:rest rdf:nil .
_:g rdf:type rdf:List .
_:i rdf:first _:c .
_:i rdf:rest _:g .
_:i rdf:type rdf:List .
_:a owl:intersectionOf _:i .
_:k rdf:type owl:Class .
_:m rdf:type owl:Class .
_:o rdf:first first:B .
_:o rdf:rest rdf:nil .
_:o rdf:type rdf:List .
_:q rdf:first first:A .
_:q rdf:rest _:o .
_:q rdf:type rdf:List .
_:m owl:unionOf _:q .
_:k owl:complementOf _:m .
_:a owl:equivalentClass _:k .
first:A rdf:type owl:Class .
first:B rdf:type owl:Class .

7.1.14. owl:equivalentProperty

LitePositive Entailment Test:001
Description: (informative) <equivalentProperty/Manifest001#test>
hasLeader may be stated to be the owl:equivalentProperty of hasHead.
N3 format is informative.
LitePremises: <equivalentProperty/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/equivalentProperty/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentProperty/premises001" >
   <owl:ObjectProperty rdf:ID="hasHead">
      <owl:equivalentProperty>
         <owl:ObjectProperty rdf:ID="hasLeader"/>
      </owl:equivalentProperty>
   </owl:ObjectProperty>
   <owl:Thing rdf:ID="X">
     <first:hasLeader>
        <owl:Thing rdf:ID="Y"/>
     </first:hasLeader>
   </owl:Thing>
</rdf:RDF>
first:hasHead rdf:type owl:ObjectProperty .
first:hasLeader rdf:type owl:ObjectProperty .
first:hasHead owl:equivalentProperty first:hasLeader .
first:X rdf:type owl:Thing .
first:Y rdf:type owl:Thing .
first:X first:hasLeader first:Y .
LiteConclusions: <equivalentProperty/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/equivalentProperty/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentProperty/conclusions001" >
   <owl:Thing rdf:about="premises001#X">
     <first:hasHead>
        <owl:Thing rdf:about="premises001#Y"/>
     </first:hasHead>
   </owl:Thing>   
   <owl:ObjectProperty rdf:about="premises001#hasHead"/>
</rdf:RDF>
first:X rdf:type owl:Thing .
first:Y rdf:type owl:Thing .
first:X first:hasHead first:Y .
first:hasHead rdf:type owl:ObjectProperty .

LitePositive Entailment Test:002
Description: (informative) <equivalentProperty/Manifest002#test>
A reasoner can also deduce that hasLeader is a subProperty of hasHead and hasHead is a subProperty of hasLeader.
N3 format is informative.
LitePremises: <equivalentProperty/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/equivalentProperty/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentProperty/premises002" >
   <owl:ObjectProperty rdf:ID="hasHead">
      <owl:equivalentProperty>
         <owl:ObjectProperty rdf:ID="hasLeader"/>
      </owl:equivalentProperty>
   </owl:ObjectProperty>
</rdf:RDF>
first:hasHead rdf:type owl:ObjectProperty .
first:hasLeader rdf:type owl:ObjectProperty .
first:hasHead owl:equivalentProperty first:hasLeader .
LiteConclusions: <equivalentProperty/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/equivalentProperty/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/equivalentProperty/conclusions002" >
   <owl:ObjectProperty rdf:about="premises002#hasHead">
      <rdfs:subPropertyOf rdf:resource="premises002#hasLeader"/>
   </owl:ObjectProperty>
   <owl:ObjectProperty rdf:about="premises002#hasLeader">
      <rdfs:subPropertyOf rdf:resource="premises002#hasHead"/>
   </owl:ObjectProperty>
</rdf:RDF>
first:hasHead rdf:type owl:ObjectProperty .
first:hasHead rdfs:subPropertyOf first:hasLeader .
first:hasLeader rdf:type owl:ObjectProperty .
first:hasLeader rdfs:subProp