Dear Pat, (01)
Oh dear! What a tangled web we weave:-) (02)
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> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
> Sent: 07 July 2012 03:09
> To: [ontolog-forum] ; Chris Menzel
> Subject: Re: [ontolog-forum] Truth
> On Jul 6, 2012, at 4:25 PM, Chris Menzel wrote:
> > On Fri, Jul 6, 2012 at 4:05 PM, Michael Brunnbauer <brunni@xxxxxxxxxxxx>
> > Hello Matthew,
> > On Fri, Jul 06, 2012 at 09:35:02PM +0100, Matthew West wrote:
> > > CM> ... classes are extensional in OWL.
> > > Is that extensional in that the extension is the members declared in
> OWL ontology, or is that extensional in the sense that the members define
> class, but I might not know about all of them?
> > I think it's extensional in the sense that classes are not first class
> > entities but defined via the extension of the rdf:type property.
> > http://www.w3.org/TR/rdf-mt/#sinterp
> > Actually, yes, there is an RDF-compatible semantics for OWL I'd
> about where OWL classes are simply entities that are assigned sets of
> individuals as their extensions. In this semantics, distinct classes can
> the same "members". But IIRC in both the W3C "direct" semantics for OWL
> the "model theoretic" semantics, OWL classes are simply sets of
> > Pat will probably jump in here and straighten me out...
> (Back from being a builder of kitchens, Pat reads lots of emails...)
> FIrst, there are several OWLs. OWL-Full is the most RDF-compatible, with
> few restrictions on what can be said in it, but has no complete reasoners
> isn't very widely used. OWL-DL has many restrictions. OWL-Full follows RDF
> RDFS in treating classes as first-class (sorry about the pun) entities and
> intensional, not extensional (in the sense that classes are not identified
> with sets, so it is consistent for two classes to have exactly the same
> members but still be distinct classes.) OWL-DL is quite different: it does
> allow classes to be first-class entities, and it assumes that classes are
> defined extensionally, i.e. are sets, ie defined by their membership. So,
> sum up:
> extensional = classes are identified with the sets of their members.
> intensional = not extensional, so having the same members does not
> identity of classes. (Put another way, classes have 'robust identity'
> independent of their membership.)
> OWL-Full: classes are individuals, just as in RDF and RDFS and Common
> Classes are intensional.
> OWL-DL: classes are not individuals, and properties (binary relations)
> relate individuals, not classes. In the language of the ISO Common Logic
> specs, OWL-DL is a segregated dialect. Classes are extensional.
> The OWL specs give a 'direct' semantics for OWL-DL (which was the only OWL
> that many of the WG cared about, those people also being not particularly
> interested in RDF) whlie allowing OWL-Full to simply be an RDF extension.
> makes for confusing reading, and is the primary reason the specs are so
> to follow..
> (There is also the newer standard OWL2-DL, which relaxes the syntax to
> apparently allow classes to contain other classes, just as in OWL-Full,
> fact it does this by a mechanism called 'punning' which keeps the
> segregation in the semantics. And it also assumes extensionality.)
> Hope this helps.
> > -chris
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