On Jul 6, 2012, at 4:25 PM, Chris Menzel wrote: (01)
> On Fri, Jul 6, 2012 at 4:05 PM, Michael Brunnbauer <brunni@xxxxxxxxxxxx>
>wrote:
>
> 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 the
>OWL ontology, or is that extensional in the sense that the members define the
>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 forgotten
>about where OWL classes are simply entities that are assigned sets of
>individuals as their extensions. In this semantics, distinct classes can have
>the same "members". But IIRC in both the W3C "direct" semantics for OWL and
>the "model theoretic" semantics, OWL classes are simply sets of individuals.
>
> Pat will probably jump in here and straighten me out... (02)
(Back from being a builder of kitchens, Pat reads lots of emails...) (03)
FIrst, there are several OWLs. OWL-Full is the most RDF-compatible, with very
few restrictions on what can be said in it, but has no complete reasoners so
isn't very widely used. OWL-DL has many restrictions. OWL-Full follows RDF and
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 not 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, to sum up: (04)
extensional = classes are identified with the sets of their members.
intensional = not extensional, so having the same members does not guarantee
identity of classes. (Put another way, classes have 'robust identity' which is
independent of their membership.) (05)
OWL-Full: classes are individuals, just as in RDF and RDFS and Common Logic.
Classes are intensional.
OWL-DL: classes are not individuals, and properties (binary relations) only
relate individuals, not classes. In the language of the ISO Common Logic specs,
OWL-DL is a segregated dialect. Classes are extensional. (06)
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. This makes for
confusing reading, and is the primary reason the specs are so hard to follow.. (07)
(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, but in
fact it does this by a mechanism called 'punning' which keeps the underlying
segregation in the semantics. And it also assumes extensionality.) (08)
Hope this helps. (09)
Pat (010)
>
> -chris
>
>
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