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Contents
Tests that show the relationship between OWL and simple arithmetic.
| Full (EC) | Positive Entailment Test: | 002 | |
|---|---|---|---|
Description:
(informative)
<extra-credit/Manifest002#test>
|
|||
| This test shows a relationship between integer multiplication and OWL Full. | |||
| Required datatype support: | xsd:int, | ||
| N3 format is informative. | |||
| Full | Premises:
<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) | Positive Entailment Test: | 003 | |
|---|---|---|---|
Description:
(informative)
<extra-credit/Manifest003#test>
|
|||
| Prime factorization can be expressed in OWL Full. | |||
| Required datatype support: | xsd:int, | ||
| N3 format is informative. | |||
| Full | Premises:
<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) | Positive Entailment Test: | 004 | |
|---|---|---|---|
Description:
(informative)
<extra-credit/Manifest004#test>
|
|||
| A more difficult prime factorization example. | |||
| Required datatype support: | xsd:int, | ||
| N3 format is informative. | |||
| Full | Premises:
<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 . | |||