Re: OWL semantics

From: Jeff Heflin <heflin@cse.lehigh.edu>
Subject: Re: OWL semantics
Date: Fri, 09 Aug 2002 14:23:32 -0400

> Ian,
> 
> I absolutely agree with you that it is of utmost importance that we
> resolve the OWL semantic issues now. That said, I'd like to discuss your
> arguments for your position.
> 
> Although there may be good reasons for being against "classes as
> instances," your argument below is not one of them. Sure, unary
> predicates are a common way to model classes in first order logic (FOL),
> but another just as common way is to define binary relations such as
> isa(x,y) (which says x isa a subclass of y) and instanceOf(x,y) (which
> says that x is an instance of class y). Only a few simple axioms are
> needed to give these relations their correct semantics. With this idiom,
> classes are no longer predicates but are instead objects in the domain
> of discourse. Furthermore, the isa and instanceOf relations have a nice
> correspondence with rdfs:subClassOf and rdf:type, making it likely that
> people translating RDF into FOL might choose this method over the unary
> predicate approach.

Sure, doing this with RDF and RDFS is fairly easy.  The difficulty comes
when you handle the rest of OWL.  Look at the treatment of DAML+OIL
restrictions in the DAML+OIL axiomatization.

> However, that said, this approach does not address the problem of
> properties as instances. Note, in the RDF model, properties are simply
> special kinds resources, and which suggests that they should be treated
> as instances as well. To do so, would require you to embed HOL in FOL.
> Perhaps your argument should focus on this matter first, before talking
> about classes as instances.

Well, if one is going the classes-as-instances route, one might as well go
along the same route for properties, as is done in the DAML+OIL
axiomatization.   It doesn't push you over into HOL.

> I strongly agree with your point 1b. The use of OWL/RDF to change the
> meaning of OWL or RDF itself could open up a Pandora's Box of trouble.
> However, I'm afraid that this might be a consequence of choosing to
> layer OWL on RDF. After all, RDF let's you say anything about anything,
> and everything is just a resource. In order to describe a class or
> property in RDF, you have to treat it as a resource, because all you
> have are classes, properties and resources. If a class isn't a resource,
> then you can't state that it is the subclass of another class. And what
> is a resource, but an instance? But with this model, how can we prevent
> statements that redefine RDF or OWL properties? Perhaps we can darken
> the entire RDF, RDFS and OWL vocabularies, but this seems to go against
> the zeitgeist of RDF. After all, if an RDF reasoner is supposed to
> conclude A subClassOf C, when it sees A foo B, B foo C, and foo
> subpropertyOf subClassOf, why shouldn't an OWL reasoner? [1] To do
> otherwise, would be a non-monotonic layering (by this I mean, a language
> that is layered on another language does not have all the entailments of
> later).

Well, if you buy into the RDF view of layering then there are indeed
problems.

> This is a crucial problem. It seems that RDF's ability to say anything
> about anything presents a great big unknown when you begin adding more
> expressiveness to the language.  In essence, I think this feature alone
> turns our work from a standardization effort into a difficult research
> problem. 

Well, it is not really a research problem.  There are lots of known
layering solutions, each of which has different tradeoffs.  The problem we
are experiencing is that different WG members have different ideas of the
right tradeoffs.

> Although dark triples may help us sweep the problem under the
> rug, I believe that approach undermines the few good reasons for
> layering on RDF in the first place, and that if we take that approach,
> we would have been better off just creating a (non-RDF) XML ontology
> language.

No comment.  :-)

> Unfortunately, I don't have any solutions at this time.

I do have a solution.  Actually several solutions, starting with the
syntax-extension solution.

> Jeff

Peter F. Patel-Schneider
Bell Labs Research

Received on Friday, 9 August 2002 23:42:36 UTC