Re: Some comments about the relationships between rdfs:subPropertyOf and rdfs:domain(rdfs:range)

>Hi,
>
>I have some comments about rdfs:subPropertyOf:
>1) if  (R rdfs:subPropertyOf S)
>      (R rdfs:domain C1)  (R rdf:range D1)
>      (S rdfs:domain C2)  (S rdf:range D2)
>   can we infer that  (C1 rdfs:subClassOf C2) && (D1 rdfs:subClassOf D2)?
>
>I believe the result can be easily inferred by the RDF Model Theory, 
>but there is no rule in the RDFS closure rules
>to show this inference.

Peter Patel-Schneider has pointed out to me that my previous reply 
may have been misleading, in that in this case it is not in fact even 
valid to infer that C1 is a subset of C2 (and similarly for the 
range). The reason is that the domain and range assertions only 
provide an upper bound on the 'true' domain and ranges, ie the sets 
of things to which the property actually apply.  Thus for example it 
would be fine to say that

ex:parentOf rdfs:domain ex:human .
ex:parentOf rdfs:range ex:human .

but this does not entail that all human beings have children, only 
that all parents (and children) are human. The 'real' domain, in the 
mathematical sense, of this property is the subset of humans who 
happen to have children, but there need be no RDFS class 
corresponding exactly to this set (and indeed there is no way in RDFS 
to specify such an 'exactly-fitting' class by if-and-only-if 
conditions; there is, however, in OWL.)

Thus, the fact that x R y entails x S y and hence that x type C2 (and 
y type D2) does not itself mean that C1 is a subset of C2; only that 
the subset of C1 which contains the actual entities to which R 
applies is a subset of C2: but since this may well be a proper subset 
of C1, no subset relationship can be inferred between C1 and C2.

Sorry if my earlier message was misleading.

Pat Hayes
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