FullSemanticsRdfsAxioms

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WORK IN PROGRESS

The changed OWL 1 Full semantics of the RDFS vocabulary.

The OWL 1 semantics for the RDFS vocabulary, e.g. rdfs:subClassOf, looks somewhat contrived. This is due to the fact that the semantic conditions given in OWL have to treat two different languages: OWL DL (RDF version), and OWL Full. For OWL 2, the style of the semantic conditions will be revised.

Sub Properties

Syntax

Semantics

Old semantics

 IF
     p, q ∈ IOOP
   OR
     p, q ∈ IODP
 THEN
     (p,q) ∈ EXT_I(S_I(rdfs:subPropertyOf))
   IF AND ONLY IF
     EXT_I(S_I(p)) ⊆ EXT_I(S_I(q))

New semantics

   (p,q) in EXT_I(S_I(rdfs:subPropertyOf))
 IF AND ONLY IF
   p, q in IOOP,
   EXT_I(p) subset EXT_I(q)

Considerations

  • The "IF" direction is, in principle, redundant, since it is already given in RDFS. But it should be there for user convenience.
  • I did not take the conditional style of definition
    • It doesn't cover the complete semantics, because the "IF" direction given in RDFS is stronger (the preconditions here are in the THEN branch there)
    • Although there are different preconditions, the main IFF condition is the same in both cases
    • The precondition with IOOP will fire anyway, the IODP precondition doesn't add any new information
    • I believe that the preconditions are there only for the OWL-DL version in §5 of AS&S. In this language, IOOP and IODP are disjoint parts of the universe. However, the strategy of using preconditions is not used for owl:equivalentClass
  • For OWL-Full, a useful additional semantic condition seems to be "IF (p,q) in EXT_I(S_I(rdfs:subPropertyOf)) AND q in IODP THEN p in IODP". However, this follows already from the above IFF semantic condition, since in this case EXT_I(p) will only contain datavalues.

Other Entries of RDFS table

analogue



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