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FullSemanticsDatatypeRestrictions
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WORK IN PROGRESS
The OWL 2 Full semantics of Datatype Restrictions, Complements, and Enumerations.
Note: There is still some ongoing discussion on syntax and semantics of these features in OWL 1 DL. However, the situation has much stabilized over the last months, so I am going to start working on this topic now.
Contents
Datatype Restrictions
Syntax
c rdf:type rdfs:Datatype c owl:onDatatype d c owl:withRestrictions SEQ( y_1 ... y_n ) y_1 xsd:facet_1 v_1 ... y_n xsd:facet_n v_n
Semantics
IF l is a sequence of y_1, ..., y_n over R_I (c,d) ∈ EXT_I(S_I(owl:onDatatype)), (c,l) ∈ EXT_I(S_I(owl:withRestrictions)), (y_1, v_1) ∈ EXT_I(S_I(xsd:facet_1)), ..., (y_n, v_n) ∈ EXT_I(S_I(xsd:facet_n)) THEN c, d ∈ IDC, v_1, ..., v_n ∈ LV_I, CEXT_I(c) = CEXT_I(d) ∩ FACET(xsd:facet_1,d,v_1) ∩ ... ∩ FACET(xsd:facet_n,d,v_n)
where FACET(xsd:facet, d, v) denotes the subset of LV_I, which is specified by applying the facet xsd:facet with value v to the extension CEXT_I(d) of the datatype d.
Special case: If the facet cannot be applied, then FACET(xsd:facet, d, v) is empty. [FIXME: Should ontology rather be inconsistent in such a case?]
Comprehension Principle:
TODO
Datatype Complements
In OWL 2 DL, the complement of a datatype is defined relative to the data domain. So this semantics has to be mirrored in OWL 2 Full.
Syntax
c rdf:type rdfs:Datatype c owl:datatypeComplementOf d
Semantics
Axiomatic triples:
owl:datatypeComplementOf rdf:type rdf:Property owl:datatypeComplementOf rdfs:domain rdfs:Datatype owl:datatypeComplementOf rdfs:range rdfs:Datatype
Main semantic condition:
(c,d) ∈ EXT_I(S_I(owl:datatypeComplementOf)) IF AND ONLY IF c, d ∈ IDC, CEXT_I(c) = LV_I - CEXT_I(d)
Comprehension Principle:
IF c ∈ IDC THEN ∃ x (x,d) ∈ EXT_I(S_I(owl:datatypeComplementOf))
Datatype Enumerations
See treetment of owl:oneOf.
Considerations
- Question: Is it right to have ONLY-IF semantics, as for "normal" restrictions?