From: Dan Connolly (connolly@w3.org)
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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