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FullSemanticsUniversalProperty
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The OWL 2 Full semantics of the Top and Bottom Property.
The Top Property is the property which relates every existing individual to every other individual.
The Bottom Property is the property which relates no individuals at all, i.e. the property which has the empty extension.
The Top and Bottom Property exist both as data properties and object properties.
Contents
Top Object Property
Syntax
x owl:TopObjectProperty y
Semantics
Axiomatic Triples:
owl:TopObjectProperty rdf:type owl:ObjectProperty owl:TopObjectProperty rdfs:domain owl:Thing owl:TopObjectProperty rdfs:range owl:Thing
Main semantic condition:
EXT_I(S_I(owl:TopObjectProperty)) = IOT×IOT
Top Data Property
Syntax
x owl:TopDataProperty y
Semantics
Axiomatic Triples:
owl:TopDataProperty rdf:type owl:DatatypeProperty owl:TopDataProperty rdfs:domain owl:Thing owl:TopDataProperty rdfs:range rdfs:Literal
Main semantic condition:
EXT_I(S_I(owl:TopDataProperty)) = IOT×LV_I
Bottom Object Property
Syntax
x owl:BottomObjectProperty y
Semantics
Axiomatic Triples:
owl:BottomObjectProperty rdf:type owl:ObjectProperty owl:BottomObjectProperty rdfs:domain owl:Nothing owl:BottomObjectProperty rdfs:range owl:Nothing
Main semantic condition:
EXT_I(S_I(owl:BottomObjectProperty)) = ∅
Bottom Data Property
Syntax
x owl:BottomDataProperty y
Semantics
Axiomatic Triples:
owl:BottomDataProperty rdf:type owl:DatatypeProperty owl:BottomDataProperty rdfs:domain owl:Nothing owl:BottomDataProperty rdfs:range owl:Nothing
Main semantic condition:
EXT_I(S_I(owl:BottomDataProperty)) = ∅
Considerations
- The main semantic conditions mirror the entries in the "Parts" table of OWL 1 Full.
- The domain and range of the Top Property follow from the main semantic condition. So domain and range are redundant in principle.
- The main semantic condition of the Bottom Property tells the same as the domain and range of the Bottom Property. So one of the two informations is redundant in principle.
- The range of the bottom data property is currently owl:Nothing. This is technically ok in OWL Full, but looks a bit strange. A bottom datatype would be helpful here.