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