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Re: new version of semantic layering document

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Mon, 23 Sep 2002 16:16:53 -0400 (EDT)
Message-Id: <20020923.161653.66646069.pfps@research.bell-labs.com>
To: phayes@ai.uwf.edu
Cc: www-webont-wg@w3.org

From: pat hayes <phayes@ai.uwf.edu>
Subject: Re: new version of semantic layering document
Date: Mon, 23 Sep 2002 14:37:31 -0500

> >On a quick read through of part of the new document I found the following
> >issues.  I'm assuming that rdfs:subClassOf, rdfs:subPropertyOf,
> >rdfs:domain, and rdfs:range are strengthened to iff.
> Yes for the subs, as the document says; no for domain and range. See 
> my message to Jeremy.

If it is ``No'' for domain and range, then there are quite a few triples in
the table near the end of section 3 that are not valid.

> BTW, strengthening domain and range to IFF seems to me to be a really 
> bad idea, in general: it completely destroys the idea of conjunctive 
> range/domain assertions. We put the current semantics into RDFS in 
> order to conform to the DAML conjunctive semantics, so why do you 
> want to blow this out of the water in OWL?

I don't understand why you are saying this?  How does making domain and
range IFF destroy the conjunctive semantics?


> OK, its easy to make that change if you prefer. It seems odd to say 
> that an empty class is disjoint with itself, is all.

Why is this odd?  


> >- In Large OWL it is not the case that owl:Class and rdfs:Class have the
> >   same extension.  In particular owl:Nothing (and indeed most empty
> >   classes) can belong to neither, either one or, or both of owl:Class and
> >   rdfs:Class in Large OWL.  It is thus not the case that IOC=IC or IOP=IP
> >   in Large OWL.
> No, wait. It is *stipulated* that IOC=IC and IOP=IP in large OWL. 
> Those equations are part of the large-OWL semantics. So it is the 
> case.

I was assuming that the definition of Large OWL was IOT=IR.  I see now that
it also requires ICO=IC and IOP=IP.


> >- There are many restrictions in Large OWL that may be problematic because
> >   their presence may affect their extension.  For example, what is the
> >   class extension of 
> >       _:x owl:onProperty rdfs:subClassOf .
> >       _:x owl:maxCardinality 57 .
> Its the class of all RDFS classes which have no more than 57 
> subclasses, right? That might be empty, for all I know. (Oh no, wait, 
> all the empty classes are in it.) But Im sure it *exists*. In fact, 
> you could toss in things like transfinite cardinalities (as long as 
> they are describable) and I would still be sure the restriction 
> classes would exist.

> >   Can it be shown that there are *no* problems in determining the class
> >   extensions of all the restrictions that mention the RDF and RDFS
> >   structural properties and that thus may interfere with their own class
> >   extension?
> Im not sure what you mean by 'interfere with'. One can certainly 
> create inconsistencies by asserting that, say, rdfs:subClassOf is the 
> same as some odd restriction. But just defining new restriction 
> classes in terms of the RDFS/OWL vocabulary doesn't in itself 
> interfere with that vocabulary in any sense I can think of.

In Large OWL the class of all classes with no more than n subclasses
exists in all interpretations, for n any non-negative integer.  Some of
these classes may be subclasses of some other of them.  Can you show that
there is not some interaction between all these classes, and other such
Large OWL restrictions, that makes it impossible to have a consistent view
of all such OWL classes?

The kind of problem that you could get into is if there was some break
point where ``less than n subclasses'' was empty but ``less than n+1
subclasses'' was not, except that the existence of  ``less than n
subclasses'' messed up this reasoning.


> >PS:  I would much have preferred to try to get a version of the previous
> >      document that didn't have any known bugs before making such drastic
> >      changes.
> Well, the previous approach seemed to be hopeless, and this is really 
> only a simplified version phrased somewhat differently. The only 
> major change was realizing that we could impose simplified 
> restriction closure conditions on large OWL, and let it support all 
> the intuitive inferences. (That is what took the weekend.)

But this is precisely where I cannot see a way of showing that the model
theory is non-trivial.


Received on Monday, 23 September 2002 16:17:02 UTC

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