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Les jeux d'essais du langage d'ontologie Web OWL

7.5.1. L'arithmétique dans OWL

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7.5.1. L'arithmétique dans OWL

Des tests qui montrent les relations entre OWL et l'arithmétique simple.

Full(EC) Test d'inférence positive : 002
Description : (informatif) <extra-credit/Manifest002#test>
Ce test montre une relation entre la multiplication d'entiers et OWL Full.
Les types de données à gestion obligatoire : xsd:int
Le format N3 est informatif.
Full Prémisses : <extra-credit/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:rdfs= "http://www.w3.org/2000/01/rdf-schema#"
    xml:base="http://www.w3.org/2002/03owlt/extra-credit/premises002" >

   <owl:FunctionalProperty rdf:ID="p-N-to-1" >
     <owl:inverseOf>
       <owl:ObjectProperty rdf:ID="invP-1-to-N" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N" />
     <rdfs:range rdf:resource="#only-d" />
   </owl:FunctionalProperty>
   <owl:FunctionalProperty rdf:ID="q-M-to-1" >
     <owl:inverseOf>
        <owl:ObjectProperty rdf:ID="invQ-1-to-M" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N-times-M" />
     <rdfs:range rdf:resource="#cardinality-N" />
   </owl:FunctionalProperty>
   <owl:FunctionalProperty rdf:ID="r-N-times-M-to-1">
     <owl:inverseOf>
        <owl:ObjectProperty  rdf:ID="invR-1-to-N-times-M" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N-times-M" />
     <rdfs:range rdf:resource="#only-d" />
   </owl:FunctionalProperty>
   
    <owl:Class rdf:ID="only-d">
      <owl:oneOf rdf:parseType="Collection">
         <rdf:Description rdf:ID="d"/>
      </owl:oneOf>
      <owl:equivalentClass>
        <owl:Restriction>
          <owl:onProperty rdf:resource="#invP-1-to-N"/>
          <owl:cardinality rdf:resource="#N"/>
        </owl:Restriction>
      </owl:equivalentClass>
      <owl:equivalentClass>
         <owl:Restriction>
           <owl:onProperty rdf:resource="#invR-1-to-N-times-M"/>
           <owl:cardinality rdf:resource="#N-times-M"/>
         </owl:Restriction>
      </owl:equivalentClass>
    </owl:Class>
    <owl:Class rdf:ID="cardinality-N">
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#p-N-to-1"/>
             <owl:someValuesFrom rdf:resource="#only-d"/>
           </owl:Restriction>
       </owl:equivalentClass>
       <owl:equivalentClass>
           <owl:Restriction>
              <owl:onProperty rdf:resource="#invQ-1-to-M"/>
              <owl:cardinality rdf:resource="#M"/>
           </owl:Restriction>
       </owl:equivalentClass>
    </owl:Class>
    <owl:Class rdf:ID="cardinality-N-times-M">
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#q-M-to-1"/>
             <owl:someValuesFrom rdf:resource="#cardinality-N"/>
           </owl:Restriction>
       </owl:equivalentClass>
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#r-N-times-M-to-1"/>
             <owl:someValuesFrom rdf:resource="#only-d"/>
           </owl:Restriction>
       </owl:equivalentClass>
    </owl:Class>

    <rdf:Description rdf:about="#N">
      <owl:sameAs 
          rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">15</owl:sameAs>
     </rdf:Description>
    <rdf:Description rdf:about="#M">
      <owl:sameAs 
          rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">23</owl:sameAs>
     </rdf:Description>

</rdf:RDF>
 
first:p-N-to-1 rdf:type owl:FunctionalProperty .
first:invP-1-to-N rdf:type owl:ObjectProperty .
first:p-N-to-1 owl:inverseOf first:invP-1-to-N .
first:p-N-to-1 rdfs:domain first:cardinality-N .
first:p-N-to-1 rdfs:range first:only-d .
first:q-M-to-1 rdf:type owl:FunctionalProperty .
first:invQ-1-to-M rdf:type owl:ObjectProperty .
first:q-M-to-1 owl:inverseOf first:invQ-1-to-M .
first:q-M-to-1 rdfs:domain first:cardinality-N-times-M .
first:q-M-to-1 rdfs:range first:cardinality-N .
first:r-N-times-M-to-1 rdf:type owl:FunctionalProperty .
first:invR-1-to-N-times-M rdf:type owl:ObjectProperty .
first:r-N-times-M-to-1 owl:inverseOf first:invR-1-to-N-times-M .
first:r-N-times-M-to-1 rdfs:domain first:cardinality-N-times-M .
first:r-N-times-M-to-1 rdfs:range first:only-d .
first:only-d rdf:type owl:Class .
_:a rdf:first first:d .
_:a rdf:rest rdf:nil .
first:only-d owl:oneOf _:a .
_:c rdf:type owl:Restriction .
_:c owl:onProperty first:invP-1-to-N .
_:c owl:cardinality first:N .
first:only-d owl:equivalentClass _:c .
_:e rdf:type owl:Restriction .
_:e owl:onProperty first:invR-1-to-N-times-M .
_:e owl:cardinality first:N-times-M .
first:only-d owl:equivalentClass _:e .
first:cardinality-N rdf:type owl:Class .
_:g rdf:type owl:Restriction .
_:g owl:onProperty first:p-N-to-1 .
_:g owl:someValuesFrom first:only-d .
first:cardinality-N owl:equivalentClass _:g .
_:i rdf:type owl:Restriction .
_:i owl:onProperty first:invQ-1-to-M .
_:i owl:cardinality first:M .
first:cardinality-N owl:equivalentClass _:i .
first:cardinality-N-times-M rdf:type owl:Class .
_:k rdf:type owl:Restriction .
_:k owl:onProperty first:q-M-to-1 .
_:k owl:someValuesFrom first:cardinality-N .
first:cardinality-N-times-M owl:equivalentClass _:k .
_:m rdf:type owl:Restriction .
_:m owl:onProperty first:r-N-times-M-to-1 .
_:m owl:someValuesFrom first:only-d .
first:cardinality-N-times-M owl:equivalentClass _:m .
first:N owl:sameAs "15"^^xsd:int  .
first:M owl:sameAs "23"^^xsd:int  .
Full Conclusions : <extra-credit/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/extra-credit/conclusions002" >

    <rdf:Description rdf:about="premises002#N-times-M">
      <owl:sameAs 
          rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">345</owl:sameAs>
     </rdf:Description>

</rdf:RDF>
 
first:N-times-M owl:sameAs "345"^^xsd:int  .

Full(EC) Test d'inférence positive : 003
Description : (informatif) <extra-credit/Manifest003#test>
On peut exprimer la factorisation d'un nombre premier dans OWL Full.
Les types de données à gestion obligatoire : xsd:int
Le format N3 est informatif.
Full Prémisses : <extra-credit/premises003> 
<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/extra-credit/premises003" >

   <owl:FunctionalProperty rdf:ID="p-N-to-1" >
     <owl:inverseOf>
       <owl:ObjectProperty rdf:ID="invP-1-to-N" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N" />
     <rdfs:range rdf:resource="#only-d" />
   </owl:FunctionalProperty>
   <owl:FunctionalProperty rdf:ID="q-M-to-1" >
     <owl:inverseOf>
        <owl:ObjectProperty rdf:ID="invQ-1-to-M" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N-times-M" />
     <rdfs:range rdf:resource="#cardinality-N" />
   </owl:FunctionalProperty>
   <owl:FunctionalProperty rdf:ID="r-N-times-M-to-1">
     <owl:inverseOf>
        <owl:ObjectProperty  rdf:ID="invR-1-to-N-times-M" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N-times-M" />
     <rdfs:range rdf:resource="#only-d" />
   </owl:FunctionalProperty>
   
    <owl:Class rdf:ID="only-d">
      <owl:oneOf rdf:parseType="Collection">
         <rdf:Description rdf:ID="d"/>
      </owl:oneOf>
      <owl:equivalentClass>
        <owl:Restriction>
          <owl:onProperty rdf:resource="#invP-1-to-N"/>
          <owl:cardinality rdf:resource="#N"/>
        </owl:Restriction>
      </owl:equivalentClass>
      <owl:equivalentClass>
         <owl:Restriction>
           <owl:onProperty rdf:resource="#invR-1-to-N-times-M"/>
           <owl:cardinality rdf:resource="#N-times-M"/>
         </owl:Restriction>
      </owl:equivalentClass>
    </owl:Class>
    <owl:Class rdf:ID="cardinality-N">
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#p-N-to-1"/>
             <owl:someValuesFrom rdf:resource="#only-d"/>
           </owl:Restriction>
       </owl:equivalentClass>
       <owl:equivalentClass>
           <owl:Restriction>
              <owl:onProperty rdf:resource="#invQ-1-to-M"/>
              <owl:cardinality rdf:resource="#M"/>
           </owl:Restriction>
       </owl:equivalentClass>
    </owl:Class>
    <owl:Class rdf:ID="cardinality-N-times-M">
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#q-M-to-1"/>
             <owl:someValuesFrom rdf:resource="#cardinality-N"/>
           </owl:Restriction>
       </owl:equivalentClass>
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#r-N-times-M-to-1"/>
             <owl:someValuesFrom rdf:resource="#only-d"/>
           </owl:Restriction>
       </owl:equivalentClass>
    </owl:Class>

    <rdf:Description rdf:about="#N-times-M">
      <owl:sameAs 
          rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">77</owl:sameAs>
     </rdf:Description>

</rdf:RDF>
 
first:p-N-to-1 rdf:type owl:FunctionalProperty .
first:invP-1-to-N rdf:type owl:ObjectProperty .
first:p-N-to-1 owl:inverseOf first:invP-1-to-N .
first:p-N-to-1 rdfs:domain first:cardinality-N .
first:p-N-to-1 rdfs:range first:only-d .
first:q-M-to-1 rdf:type owl:FunctionalProperty .
first:invQ-1-to-M rdf:type owl:ObjectProperty .
first:q-M-to-1 owl:inverseOf first:invQ-1-to-M .
first:q-M-to-1 rdfs:domain first:cardinality-N-times-M .
first:q-M-to-1 rdfs:range first:cardinality-N .
first:r-N-times-M-to-1 rdf:type owl:FunctionalProperty .
first:invR-1-to-N-times-M rdf:type owl:ObjectProperty .
first:r-N-times-M-to-1 owl:inverseOf first:invR-1-to-N-times-M .
first:r-N-times-M-to-1 rdfs:domain first:cardinality-N-times-M .
first:r-N-times-M-to-1 rdfs:range first:only-d .
first:only-d rdf:type owl:Class .
_:a rdf:first first:d .
_:a rdf:rest rdf:nil .
first:only-d owl:oneOf _:a .
_:c rdf:type owl:Restriction .
_:c owl:onProperty first:invP-1-to-N .
_:c owl:cardinality first:N .
first:only-d owl:equivalentClass _:c .
_:e rdf:type owl:Restriction .
_:e owl:onProperty first:invR-1-to-N-times-M .
_:e owl:cardinality first:N-times-M .
first:only-d owl:equivalentClass _:e .
first:cardinality-N rdf:type owl:Class .
_:g rdf:type owl:Restriction .
_:g owl:onProperty first:p-N-to-1 .
_:g owl:someValuesFrom first:only-d .
first:cardinality-N owl:equivalentClass _:g .
_:i rdf:type owl:Restriction .
_:i owl:onProperty first:invQ-1-to-M .
_:i owl:cardinality first:M .
first:cardinality-N owl:equivalentClass _:i .
first:cardinality-N-times-M rdf:type owl:Class .
_:k rdf:type owl:Restriction .
_:k owl:onProperty first:q-M-to-1 .
_:k owl:someValuesFrom first:cardinality-N .
first:cardinality-N-times-M owl:equivalentClass _:k .
_:m rdf:type owl:Restriction .
_:m owl:onProperty first:r-N-times-M-to-1 .
_:m owl:someValuesFrom first:only-d .
first:cardinality-N-times-M owl:equivalentClass _:m .
first:N-times-M owl:sameAs "77"^^xsd:int  .
Full Conclusions : <extra-credit/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/extra-credit/conclusions003" >
    
    <owl:Class>
         <owl:oneOf rdf:parseType="Collection">
            <rdf:Description rdf:about="premises003#N"/>
            <rdf:Description rdf:about="premises003#M"/>
         </owl:oneOf>
         <owl:oneOf rdf:parseType="Collection">
            <rdf:Description>
              <owl:sameAs rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">7</owl:sameAs>
            </rdf:Description>
            <rdf:Description>
              <owl:sameAs rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">11</owl:sameAs>
            </rdf:Description>
         </owl:oneOf>
    </owl:Class>
</rdf:RDF>
 
_:a rdf:type owl:Class .
_:c rdf:first first:M .
_:c rdf:rest rdf:nil .
_:e rdf:first first:N .
_:e rdf:rest _:c .
_:a owl:oneOf _:e .
_:g owl:sameAs "7"^^xsd:int  .
_:i owl:sameAs "11"^^xsd:int  .
_:k rdf:first _:i .
_:k rdf:rest rdf:nil .
_:m rdf:first _:g .
_:m rdf:rest _:k .
_:a owl:oneOf _:m .

Full(EC) Test d'inférence positive : 004
Description : (informatif) <extra-credit/Manifest004#test>
Un exemple de factorisation de nombre premier plus difficile.
Les types de données à gestion obligatoire : xsd:int
Le format N3 est informatif.
Full Prémisses : <extra-credit/premises004> 
<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/extra-credit/premises004" 
    xmlns:rdfs= "http://www.w3.org/2000/01/rdf-schema#">

   <owl:FunctionalProperty rdf:ID="p-N-to-1" >
     <owl:inverseOf>
       <owl:ObjectProperty rdf:ID="invP-1-to-N" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N" />
     <rdfs:range rdf:resource="#only-d" />
   </owl:FunctionalProperty>
   <owl:FunctionalProperty rdf:ID="q-M-to-1" >
     <owl:inverseOf>
        <owl:ObjectProperty rdf:ID="invQ-1-to-M" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N-times-M" />
     <rdfs:range rdf:resource="#cardinality-N" />
   </owl:FunctionalProperty>
   <owl:FunctionalProperty rdf:ID="r-N-times-M-to-1">
     <owl:inverseOf>
        <owl:ObjectProperty  rdf:ID="invR-1-to-N-times-M" />
     </owl:inverseOf>
     <rdfs:domain rdf:resource="#cardinality-N-times-M" />
     <rdfs:range rdf:resource="#only-d" />
   </owl:FunctionalProperty>
   
    <owl:Class rdf:ID="only-d">
      <owl:oneOf rdf:parseType="Collection">
         <rdf:Description rdf:ID="d"/>
      </owl:oneOf>
      <owl:equivalentClass>
        <owl:Restriction>
          <owl:onProperty rdf:resource="#invP-1-to-N"/>
          <owl:cardinality rdf:resource="#N"/>
        </owl:Restriction>
      </owl:equivalentClass>
      <owl:equivalentClass>
         <owl:Restriction>
           <owl:onProperty rdf:resource="#invR-1-to-N-times-M"/>
           <owl:cardinality rdf:resource="#N-times-M"/>
         </owl:Restriction>
      </owl:equivalentClass>
    </owl:Class>
    <owl:Class rdf:ID="cardinality-N">
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#p-N-to-1"/>
             <owl:someValuesFrom rdf:resource="#only-d"/>
           </owl:Restriction>
       </owl:equivalentClass>
       <owl:equivalentClass>
           <owl:Restriction>
              <owl:onProperty rdf:resource="#invQ-1-to-M"/>
              <owl:cardinality rdf:resource="#M"/>
           </owl:Restriction>
       </owl:equivalentClass>
    </owl:Class>
    <owl:Class rdf:ID="cardinality-N-times-M">
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#q-M-to-1"/>
             <owl:someValuesFrom rdf:resource="#cardinality-N"/>
           </owl:Restriction>
       </owl:equivalentClass>
       <owl:equivalentClass>
           <owl:Restriction>
             <owl:onProperty rdf:resource="#r-N-times-M-to-1"/>
             <owl:someValuesFrom rdf:resource="#only-d"/>
           </owl:Restriction>
       </owl:equivalentClass>
    </owl:Class>
   
    <rdf:Description rdf:about="#N-times-M">
      <owl:sameAs 
          rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">929136997</owl:sameAs>
     </rdf:Description>

</rdf:RDF>
 
first:p-N-to-1 rdf:type owl:FunctionalProperty .
first:invP-1-to-N rdf:type owl:ObjectProperty .
first:p-N-to-1 owl:inverseOf first:invP-1-to-N .
first:p-N-to-1 rdfs:domain first:cardinality-N .
first:p-N-to-1 rdfs:range first:only-d .
first:q-M-to-1 rdf:type owl:FunctionalProperty .
first:invQ-1-to-M rdf:type owl:ObjectProperty .
first:q-M-to-1 owl:inverseOf first:invQ-1-to-M .
first:q-M-to-1 rdfs:domain first:cardinality-N-times-M .
first:q-M-to-1 rdfs:range first:cardinality-N .
first:r-N-times-M-to-1 rdf:type owl:FunctionalProperty .
first:invR-1-to-N-times-M rdf:type owl:ObjectProperty .
first:r-N-times-M-to-1 owl:inverseOf first:invR-1-to-N-times-M .
first:r-N-times-M-to-1 rdfs:domain first:cardinality-N-times-M .
first:r-N-times-M-to-1 rdfs:range first:only-d .
first:only-d rdf:type owl:Class .
_:a rdf:first first:d .
_:a rdf:rest rdf:nil .
first:only-d owl:oneOf _:a .
_:c rdf:type owl:Restriction .
_:c owl:onProperty first:invP-1-to-N .
_:c owl:cardinality first:N .
first:only-d owl:equivalentClass _:c .
_:e rdf:type owl:Restriction .
_:e owl:onProperty first:invR-1-to-N-times-M .
_:e owl:cardinality first:N-times-M .
first:only-d owl:equivalentClass _:e .
first:cardinality-N rdf:type owl:Class .
_:g rdf:type owl:Restriction .
_:g owl:onProperty first:p-N-to-1 .
_:g owl:someValuesFrom first:only-d .
first:cardinality-N owl:equivalentClass _:g .
_:i rdf:type owl:Restriction .
_:i owl:onProperty first:invQ-1-to-M .
_:i owl:cardinality first:M .
first:cardinality-N owl:equivalentClass _:i .
first:cardinality-N-times-M rdf:type owl:Class .
_:k rdf:type owl:Restriction .
_:k owl:onProperty first:q-M-to-1 .
_:k owl:someValuesFrom first:cardinality-N .
first:cardinality-N-times-M owl:equivalentClass _:k .
_:m rdf:type owl:Restriction .
_:m owl:onProperty first:r-N-times-M-to-1 .
_:m owl:someValuesFrom first:only-d .
first:cardinality-N-times-M owl:equivalentClass _:m .
first:N-times-M owl:sameAs "929136997"^^xsd:int  .
Full Conclusions : <extra-credit/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/extra-credit/conclusions004" >
    
    <owl:Class>
         <owl:oneOf rdf:parseType="Collection">
            <rdf:Description rdf:about="premises004#N"/>
            <rdf:Description rdf:about="premises004#M"/>
         </owl:oneOf>
         <owl:oneOf rdf:parseType="Collection">
            <rdf:Description>
              <owl:sameAs rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">83563</owl:sameAs>
            </rdf:Description>
            <rdf:Description>
              <owl:sameAs rdf:datatype=
"http://www.w3.org/2001/XMLSchema#int">11119</owl:sameAs>
            </rdf:Description>
         </owl:oneOf>
    </owl:Class>
</rdf:RDF>
 
_:a rdf:type owl:Class .
_:c rdf:first first:M .
_:c rdf:rest rdf:nil .
_:e rdf:first first:N .
_:e rdf:rest _:c .
_:a owl:oneOf _:e .
_:g owl:sameAs "83563"^^xsd:int  .
_:i owl:sameAs "11119"^^xsd:int  .
_:k rdf:first _:i .
_:k rdf:rest rdf:nil .
_:m rdf:first _:g .
_:m rdf:rest _:k .
_:a owl:oneOf _:m .

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