On Jul 7, 2012, at 12:54 PM, Chris Mungall wrote: (01)
>
> On Jul 6, 2012, at 7:08 PM, Pat Hayes wrote:
>
>>
>> On Jul 6, 2012, at 4:25 PM, Chris Menzel wrote:
>>
>>> 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...
>>
>> (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
>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:
>> 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.)
>>
>> 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.
>
> To be pedantic - in OWL-DL there are object properties (individual to
>individual), data properties (individuals to literals) and annotation
>properties (these are invisible in the direct semantics, but in practical
>terms these can link classes, provided you don't need inferences from them) (02)
Yes. I was deliberately ignoring the annotation properties, which have ne
semantics so aren't really in the logic at all, and also ignoring the
individual/literal distinction, which is semantically meaningless and vanishes
when you put this back into a normal logical framework. (Literals are just
terms consisting of a function applied to a character string.) (03)
Pat (04)
>
> Regarding classes being the same as their extents in OWL: I don't think this
>view is universally shared. In fact, one of the authors of the OWL2 direct
>semantics specification states otherwise here:
> http://ontogenesis.knowledgeblog.org/1004
>
>> 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..
>
> Indeed!
>
>> (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.)
>>
>> Hope this helps.
>>
>> Pat
>>
>>
>>>
>>> -chris
>>>
>>>
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