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| DL | Positive Entailment Test: | 901 | |
|---|---|---|---|
Description:
(informative)
<description-logic/Manifest901#test>
|
|||
| This entailment can be replicated for any three natural numbers i, j, k such that i+j >= k. In this example, they are chosen as 2, 3 and 5. | |||
| N3 format is informative. | |||
| DL | Premises:
<description-logic/premises901>
| ||
<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/description-logic/premises901" >
<owl:ObjectProperty rdf:ID="r"/>
<owl:ObjectProperty rdf:ID="p">
<rdfs:subPropertyOf rdf:resource="#r"/>
<rdfs:range>
<owl:Class rdf:ID="A"/>
</rdfs:range>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="q">
<rdfs:subPropertyOf rdf:resource="#r"/>
<rdfs:range>
<owl:Class rdf:ID="B"/>
</rdfs:range>
</owl:ObjectProperty>
<owl:Class rdf:about="#A">
<owl:disjointWith rdf:resource="#B"/>
</owl:Class>
</rdf:RDF> | |||
first:r rdf:type owl:ObjectProperty . first:p rdf:type owl:ObjectProperty . first:p rdfs:subPropertyOf first:r . first:A rdf:type owl:Class . first:p rdfs:range first:A . first:q rdf:type owl:ObjectProperty . first:q rdfs:subPropertyOf first:r . first:B rdf:type owl:Class . first:q rdfs:range first:B . first:A rdf:type owl:Class . first:A owl:disjointWith first:B . | |||
| DL | Conclusions:
<description-logic/conclusions901>
| ||
<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/description-logic/premises901#"
xmlns:second="http://www.w3.org/2002/03owlt/description-logic/conclusions901#"
xml:base="http://www.w3.org/2002/03owlt/description-logic/conclusions901" >
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises901#p"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>2</owl:minCardinality>
</owl:Restriction>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises901#q"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>3</owl:minCardinality>
</owl:Restriction>
</owl:intersectionOf>
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises901#r"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>5</owl:minCardinality>
</owl:Restriction>
</rdfs:subClassOf>
</owl:Class>
</rdf:RDF> | |||
_:a rdf:type owl:Class . _:c rdf:type owl:Restriction . first:p rdf:type owl:ObjectProperty . _:c owl:onProperty first:p . _:c owl:minCardinality "2"^^xsd:nonNegativeInteger . _:e rdf:type owl:Restriction . first:q rdf:type owl:ObjectProperty . _:e owl:onProperty first:q . _:e owl:minCardinality "3"^^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 . _:k rdf:type owl:Restriction . first:r rdf:type owl:ObjectProperty . _:k owl:onProperty first:r . _:k owl:minCardinality "5"^^xsd:nonNegativeInteger . _:a rdfs:subClassOf _:k . | |||
| DL | Negative Entailment Test: | 902 | |
|---|---|---|---|
Description:
(informative)
<description-logic/Manifest902#test>
|
|||
| This non-entailment can be replicated for any three natural numbers i, j, k such that i+j < k. In this example, they are chosen as 2, 3 and 6. | |||
| N3 format is informative. | |||
| DL | Premises:
<description-logic/premises902>
| ||
<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/description-logic/premises902" >
<owl:ObjectProperty rdf:ID="r"/>
<owl:ObjectProperty rdf:ID="p">
<rdfs:subPropertyOf rdf:resource="#r"/>
<rdfs:range>
<owl:Class rdf:ID="A"/>
</rdfs:range>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="q">
<rdfs:subPropertyOf rdf:resource="#r"/>
<rdfs:range>
<owl:Class rdf:ID="B"/>
</rdfs:range>
</owl:ObjectProperty>
<owl:Class rdf:about="#A">
<owl:disjointWith rdf:resource="#B"/>
</owl:Class>
</rdf:RDF> | |||
first:r rdf:type owl:ObjectProperty . first:p rdf:type owl:ObjectProperty . first:p rdfs:subPropertyOf first:r . first:A rdf:type owl:Class . first:p rdfs:range first:A . first:q rdf:type owl:ObjectProperty . first:q rdfs:subPropertyOf first:r . first:B rdf:type owl:Class . first:q rdfs:range first:B . first:A rdf:type owl:Class . first:A owl:disjointWith first:B . | |||
| DL | Conclusions:
<description-logic/nonconclusions902>
| ||
<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/description-logic/nonconclusions902" >
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises902#p"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>2</owl:minCardinality>
</owl:Restriction>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises902#q"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>3</owl:minCardinality>
</owl:Restriction>
</owl:intersectionOf>
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises902#r"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>6</owl:minCardinality>
</owl:Restriction>
</rdfs:subClassOf>
</owl:Class>
</rdf:RDF> | |||
_:a rdf:type owl:Class . _:c rdf:type owl:Restriction . first:p rdf:type owl:ObjectProperty . _:c owl:onProperty first:p . _:c owl:minCardinality "2"^^xsd:nonNegativeInteger . _:e rdf:type owl:Restriction . first:q rdf:type owl:ObjectProperty . _:e owl:onProperty first:q . _:e owl:minCardinality "3"^^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 . _:k rdf:type owl:Restriction . first:r rdf:type owl:ObjectProperty . _:k owl:onProperty first:r . _:k owl:minCardinality "6"^^xsd:nonNegativeInteger . _:a rdfs:subClassOf _:k . | |||
| DL | Positive Entailment Test: | 903 | |
|---|---|---|---|
Description:
(informative)
<description-logic/Manifest903#test>
|
|||
| This entailment can be replicated for any three natural numbers i, j, k such that i+j >= k. In this example, they are chosen as 200, 300 and 500. | |||
| N3 format is informative. | |||
| DL | Premises:
<description-logic/premises903>
| ||
<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/description-logic/premises903" >
<owl:ObjectProperty rdf:ID="r"/>
<owl:ObjectProperty rdf:ID="p">
<rdfs:subPropertyOf rdf:resource="#r"/>
<rdfs:range>
<owl:Class rdf:ID="A"/>
</rdfs:range>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="q">
<rdfs:subPropertyOf rdf:resource="#r"/>
<rdfs:range>
<owl:Class rdf:ID="B"/>
</rdfs:range>
</owl:ObjectProperty>
<owl:Class rdf:about="#A">
<owl:disjointWith rdf:resource="#B"/>
</owl:Class>
</rdf:RDF> | |||
first:r rdf:type owl:ObjectProperty . first:p rdf:type owl:ObjectProperty . first:p rdfs:subPropertyOf first:r . first:A rdf:type owl:Class . first:p rdfs:range first:A . first:q rdf:type owl:ObjectProperty . first:q rdfs:subPropertyOf first:r . first:B rdf:type owl:Class . first:q rdfs:range first:B . first:A rdf:type owl:Class . first:A owl:disjointWith first:B . | |||
| DL | Conclusions:
<description-logic/conclusions903>
| ||
<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/description-logic/premises903#"
xmlns:second="http://www.w3.org/2002/03owlt/description-logic/conclusions903#"
xml:base="http://www.w3.org/2002/03owlt/description-logic/conclusions903" >
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises903#p"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>200</owl:minCardinality>
</owl:Restriction>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises903#q"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>300</owl:minCardinality>
</owl:Restriction>
</owl:intersectionOf>
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises903#r"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>500</owl:minCardinality>
</owl:Restriction>
</rdfs:subClassOf>
</owl:Class>
</rdf:RDF> | |||
_:a rdf:type owl:Class . _:c rdf:type owl:Restriction . first:p rdf:type owl:ObjectProperty . _:c owl:onProperty first:p . _:c owl:minCardinality "200"^^xsd:nonNegativeInteger . _:e rdf:type owl:Restriction . first:q rdf:type owl:ObjectProperty . _:e owl:onProperty first:q . _:e owl:minCardinality "300"^^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 . _:k rdf:type owl:Restriction . first:r rdf:type owl:ObjectProperty . _:k owl:onProperty first:r . _:k owl:minCardinality "500"^^xsd:nonNegativeInteger . _:a rdfs:subClassOf _:k . | |||
| DL | Negative Entailment Test: | 904 | |
|---|---|---|---|
Description:
(informative)
<description-logic/Manifest904#test>
|
|||
| This non-entailment can be replicated for any three natural numbers i, j, k such that i+j < k. In this example, they are chosen as 200, 300 and 600. | |||
| N3 format is informative. | |||
| DL | Premises:
<description-logic/premises904>
| ||
<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/description-logic/premises904" >
<owl:ObjectProperty rdf:ID="r"/>
<owl:ObjectProperty rdf:ID="p">
<rdfs:subPropertyOf rdf:resource="#r"/>
<rdfs:range>
<owl:Class rdf:ID="A"/>
</rdfs:range>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="q">
<rdfs:subPropertyOf rdf:resource="#r"/>
<rdfs:range>
<owl:Class rdf:ID="B"/>
</rdfs:range>
</owl:ObjectProperty>
<owl:Class rdf:about="#A">
<owl:disjointWith rdf:resource="#B"/>
</owl:Class>
</rdf:RDF> | |||
first:r rdf:type owl:ObjectProperty . first:p rdf:type owl:ObjectProperty . first:p rdfs:subPropertyOf first:r . first:A rdf:type owl:Class . first:p rdfs:range first:A . first:q rdf:type owl:ObjectProperty . first:q rdfs:subPropertyOf first:r . first:B rdf:type owl:Class . first:q rdfs:range first:B . first:A rdf:type owl:Class . first:A owl:disjointWith first:B . | |||
| DL | Conclusions:
<description-logic/nonconclusions904>
| ||
<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/description-logic/nonconclusions904" >
<owl:Class>
<owl:intersectionOf rdf:parseType="Collection">
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises904#p"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>200</owl:minCardinality>
</owl:Restriction>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises904#q"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>300</owl:minCardinality>
</owl:Restriction>
</owl:intersectionOf>
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="premises904#r"/>
</owl:onProperty>
<owl:minCardinality rdf:datatype=
"http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
>600</owl:minCardinality>
</owl:Restriction>
</rdfs:subClassOf>
</owl:Class>
</rdf:RDF> | |||
_:a rdf:type owl:Class . _:c rdf:type owl:Restriction . first:p rdf:type owl:ObjectProperty . _:c owl:onProperty first:p . _:c owl:minCardinality "200"^^xsd:nonNegativeInteger . _:e rdf:type owl:Restriction . first:q rdf:type owl:ObjectProperty . _:e owl:onProperty first:q . _:e owl:minCardinality "300"^^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 . _:k rdf:type owl:Restriction . first:r rdf:type owl:ObjectProperty . _:k owl:onProperty first:r . _:k owl:minCardinality "600"^^xsd:nonNegativeInteger . _:a rdfs:subClassOf _:k . | |||