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Re: [ontolog-forum] Ontology of Rough Sets

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 25 Jan 2011 10:56:58 -0600
Message-id: <10692BDF-38EC-454C-B6BB-EC0DBEA19C4F@xxxxxxxx>
On Jan 25, 2011, at 2:18 AM, Pat Hayes wrote:
On Jan 22, 2011, at 8:41 PM, Christopher Menzel wrote:
On Jan 22, 2011, at 6:16 PM, Pat Hayes wrote:
Slight amplification and very minor correction:
On Jan 18, 2011, at 5:58 PM, Christopher Menzel wrote:
The semantics of OWL per se does not accommodate the idea of a class's extension changing over time, although one could presumably capture the idea formally by means of a series of interpretations (thought of as temporally ordered) that assign different extensions to the same class.  (This is possible because classes are not defined to be identical to their extensions in the semantics.

This last statement is true for OWL-Full but not for OWL-DL.

Eh?  Is it not the case in the semantics for both OWL DL and OWL Full that OWL classes are simply introduced as the members of a distinguished set and that said classes are assigned extensions by the CEXT function?  What am I missing?

OWL-DL actually has two model theories:

Hm, why is this?  [LATER:] Oh, I guess you sort of answer this below...

a 'direct' one which applies to the OWL abstract syntax (in more modern terms, the 'manchester syntax' ) directly, and a model theory based on the RDF model theory for the RDF embedding of the OWL.

OK, the "direct" semantics, I take it is here:  http://www.w3.org/TR/owl-semantics/direct.html

And the RDF-based semantics here:  http://www.w3.org/TR/owl-semantics/rdfs.html

The second uses a CEXT mapping, of course, but imposes a strict extensionality condition upon it, so that one cannot have two different classes with the same extension.

Can you point this restriction out to me in the document? I simply cannot find it.  The only restrictions I see are the pairwise disjointness condition on the different semantic classes and the restriction on disallowed vocabulary. I don't see how either of these entails an extensionality condition on classes.

The former is a conventional model theory which maps class names directly to extensions. And the spec says that the former, not the latter, is normative, by the way.

So it does. I'd always assumed the two would be exactly equivalent, but I guess perhaps this isn't quite true.

So OWL-DL (as opposed to OWL-Full) is really not a 'CL/RDF-style' model theory at all, or is so only as an afterthought, and only by imposing the extensionality condition which in effect removes the flexibility to which you are appealing here.

As Ed said, much of standards work is politics. This situation was a political compromise made in order to allow the OWL specs to be written at all. One camp wanted to sever OWL from RDF altogether; the other wanted it to be solely an RDF extension. What we have is a horse designed by a committee.

Interesting, thanks of the insider insights!


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