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# OWL Web Ontology Language Test Cases7.5.1. Arithmetic in OWL

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### 7.5.1. Arithmetic in OWL

Tests that show the relationship between OWL and simple arithmetic.

 Positive Entailment Test: 002 Full (EC) Description: (informative) `` This test shows a relationship between integer multiplication and OWL Full. Required datatype support: xsd:int, N3 format is informative. Full Premises: `` ``` 15 23 ``` ```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: `` ``` 345 ``` ```first:N-times-M owl:sameAs "345"^^xsd:int . ```

 Positive Entailment Test: 003 Full (EC) Description: (informative) `` Prime factorization can be expressed in OWL Full. Required datatype support: xsd:int, N3 format is informative. Full Premises: `` ``` 77 ``` ```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: `` ``` 7 11 ``` ```_: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 . ```

 Positive Entailment Test: 004 Full (EC) Description: (informative) `` A more difficult prime factorization example. Required datatype support: xsd:int, N3 format is informative. Full Premises: `` ``` 929136997 ``` ```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: `` ``` 83563 11119 ``` ```_: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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