Re: Can we layer a DAML+OIL model theory on top of RDF?

From: Peter F. Patel-Schneider (pfps@research.bell-labs.com)
Date: 11/22/01


From: Dan Connolly <connolly@w3.org>
Subject: Re: Can we layer a DAML+OIL model theory on top of RDF?
Date: Thu, 22 Nov 2001 08:52:27 -0600

> "Peter F. Patel-Schneider" wrote:

[...]

> > 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.

Unfortunately, I don't see how to drive one through.

> > 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.

You are right.  This entailment would work, but how about switching the
intersected classes?  That doesn't work.  If RDF had unordered sets,
it could work, but more-complex examples will cause it to fail. (Think of
(A intersection B) union C versus  (A union B) intersection (A union C).)

> > 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.

I don't think that this approach works.  It only works for RDF and RDFS
because of their conjunctive, atomic status.  (That is the meaning of a
collection of triples is just the gathering of the independant, atomic
meaning of each of the triples.)

> >  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.

I am.  

> -- 
> Dan Connolly, W3C http://www.w3.org/People/Connolly/

peter


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