From: Dan Connolly ([email protected])
Date: 11/22/01
"Peter F. Patel-Schneider" wrote: > > I don't think so, because of the triples generated by DAML+OIL logical > constructs. > > For example, consider > > <rdfs:Class foo> > <daml:intersectionOf rdf:parseType="daml:collection"> > <daml:Class rdf:about="Man"> > <daml:Class rdf:about="Woman"> > </daml:intersectionOf> > </rdfs:Class> > > This does not RDFS entail > > <rdfs:Class foo> > <daml:intersectionOf rdf:parseType="daml:collection"> > <daml:Class rdf:about="Woman"> > <daml:Class rdf:about="Man"> > </daml:intersectionOf> > </rdfs:Class> > > because the RDF-encoding of the collections involved. That's not surprising; RDFS-entialment is "bigger" than RDF-entailment, and I expect DAML+OIL-entailment to be "bigger" than RDFS-entailment likewise. > Now, maybe we can live with this, as we don't really want to ask about > entailment between classes. er... I don't know what "entialment between classes" is, but I certainly want entailment between formulas about classes. > However, if we add > > <foo rdf:about="John"/> > > to both examples. The entailment is still not there. Given a suitable model theory, I expect it is. > This is much more serious. > > Even more serious is that > > <rdfs:Class foo> > <daml:intersectionOf rdf:parseType="daml:collection"> > <daml:Class rdf:about="Man"> > <daml:Class rdf:about="Woman"> > </daml:intersectionOf> > </rdfs:Class> > > <foo rdf:about="John"/> > > does not entail > > <foo rdf:about="John" > <rdf:type> > <daml:intersectionOf rdf:parseType="daml:collection"> > <daml:Class rdf:about="Man"> > <daml:Class rdf:about="Woman"> > </daml:intersectionOf> > </rdf:type> > </foo> > > this time because of the extra logical stuff attached to John. I don't see why this entialment wouldn't be there: we can show that the the two existential variables for the intersection class denote the same class, and hence the RDFS axioms about rdf:type and rdfs:Class make the entialment happen. > How can this be fixed? About the only way I can see is to not produce > RDF graph structure for the DAML+OIL logical stuff. The way I see it, they all have a common model theory: it's roughly FOL less the law of the excluded middle (property formalizing daml:imports requires a whole bunch more stuff, but I can wait on that). "RDF-entailment", then, is entailment given that model theory plus a very few axioms like (forall (?p ?s ?o) (implies (?p ?s ?o) (rdf:type ?p rdf:Predicate))) "RDFS-entialment" is entailment given that model theory plus axioms for domain/range/subClassOf/subPropertyOf etc. DAML+OIL entailment would add axioms for lists, intersection, etc. > However, this is very > hard if we start with RDF triples, as how to we tell which triples are > logical and which are not? > > The situation is *much* better if we start with XML, as then we know where > we stand. Speak for yourself. -- Dan Connolly, W3C http://www.w3.org/People/Connolly/
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