Re: S&AS: not enough type statements OWL Full-entailed from empty RDF graph

Subject: S&AS: not enough type statements OWL Full-entailed from empty RDF graph
Date: Thu, 10 Apr 2003 15:56:27 +0200

> In my last review of S&AS, just before the decision to go 
> to last call (see [1] and the discussion that followed)
> I noted that in the definition of OWL interpretations
> IC needs to be given more elements, to become completely
> consistent with the editor's version of the RDF Semantics
> document.
> It was agreed to take this up later when the next version
> of the RDF Semantics document becomes more official.
> However, only after the decision to go to last call
> I realized that exactly the same changes can also be 
> motivated by means of test cases, in a way that does not 
> depend on the semantic theory.
> Namely, a certain analogy between RDF entailment, 
> RDFS entailment, and OWL Full entailment is not complete.
> Recall that each RDF graph (including the empty RDF graph)
> RDF-entails the RDF statement
>   rdf:type rdf:type rdf:Property .,   and
> RDFS-entails RDF statements like
>   rdfs:domain rdf:type rdf:Property .
>   rdfs:Class rdf:type rdfs:Class .
>   etc.
> To summarize, each RDF(S) vocabulary element that is clearly a 
> property or class, is defined as a property or class in this way 
> with an entailed explicit RDF statement.
> However, this holds to a large extent, but does not hold completely, 
> for OWL Full.
> From the empty graph, there is OWL Full-entailment of RDF statements 
> like
>   owl:sameIndividualAs rdf:type rdf:Property .
>   owl:Thing rdf:type rdfs:Class .
> and very many other statements like this, but it seems that the
> following 12 statements are not OWL Full-entailed, given the
> definition in the last call version of S&AS:

>   owl:Class rdf:type rdf:Class .
>   owl:Restriction rdf:type rdf:Class .
>   owl:DatatypeProperty rdf:type rdf:Class .
>   owl:AnnotationProperty rdf:type rdf:Class .
>   owl:OntologyProperty rdf:type rdf:Class .

I think that the above are entailed, because in all OWL interpretations
they have instances, and thus are classes.

>   owl:ObjectProperty rdf:type rdf:Class .

The above are not be entailed in OWL DL, but are in OWL Full.

>   owl:Ontology rdf:type rdf:Class .
>   owl:AllDifferent rdf:type rdf:Class .
>   owl:FunctionalProperty rdf:type rdf:Class .
>   owl:InverseFunctionalProperty rdf:type rdf:Class .
>   owl:SymmetricProperty rdf:type rdf:Class .
>   owl:TransitiveProperty rdf:type rdf:Class .

The above are not entailed.

> It is interesting to note that the requirement that
> ICEXT has IC as domain necessarily leads to exactly the correction
> of these omissions.

I don't believe that this would change the situation.  

I propose augmenting the common semantic conditions to fix these issues.


> ==
> For future reference I recall from my review the summary of changes 
> required to S&AS :
> Replace the sentence
> >CEXTI is then defined as CEXTI(c) = ...
> by the following two sentences:
> "CI, the set of classes, is defined by
> CI = {x in RI | <x,SI(rdfs:Class)> is in EXTI(SI(rdf:type)>}.
> CEXTI is a mapping from CI to P(RI), defined for each
> c in CI by CEXTI(c) = [exactly what is already in the text].
> "
> The first table, "Conditions concerning the parts of the OWL
> universe and syntactic categories" needs to be completed
> in connection with CI:  Each of the 11 empty cells in the
> first column (SI(E) is in ...) needs to be filled with the
> set CI.  Otherwise, as discussed before, many invocations
> of CEXTI that occur later are are not clearly legal.
> (For two of these cells, for rdfs:Datatype and rdf:List,
> this amounts to a repetition from the RDF Semantics document.)
> I believe that five more lines need to be added to this table,
> for the following vocabulary elements
> (the reason is, as before, that otherwise it is not clear
> that various function invocations occurring later are legal):
> If  E is                      .SI(E). .CEXTI(SI(E)).    and
>   owl:Datarange                 CI       ?      ? subsetof CI
>   owl:SymmetricProperty         CI       ?      ? subsetof IOP
>   owl:FunctionalProperty        CI       ?      ? subsetof IOP
>   owl:InverseFunctionalProperty CI       ?      ? subsetof IOP
>   owl:TransitiveProperty        CI       ?      ? subsetof IOP
> Where I put question mark it would be most natural to define new
> specific sets, in analogy to many other sets already defined.
> I checked that the appendix remains completely consistent: each 
> invocation of CEXTI done there is legal when these changes 
> are made.
> ==
> (I am taking up the other point that Peter arose in connection with
> my review of S&AS in relation to RDF Semantics, whether 
> IC and ICEXT are part of the definition of RDFS-interpretation, 
> on rdf-comments.)
> Herman ter Horst

Received on Thursday, 10 April 2003 11:08:53 UTC