On Jul 8, 2012, at 8:34 AM, David Price wrote: (01)
>
> On 8 Jul 2012, at 03:52, Pat Hayes wrote:
>
>>
>> On Jul 7, 2012, at 12:54 PM, Chris Mungall wrote:
>>
>>>
>>> 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)
>>>
>>> Regarding classes being the same as their extents in OWL: I don't think
>this view is universally shared.
>>
>> Well, I havnt checked the OWL2 specs in detail, I confess, but it is
>certainly true in the original OWL-DL, stated quite explicitly in the
>semantics. Mathematical statements in a normative specification are,
>fortunately, not "views" to be shared or not, at will.
>
>
> The OWL 1 Language Reference says: (02)
Yes, this is for all the OWLs, so to speak, as a general statement. OWL Full
does indeed treat classes intensionally. OWL-DL, however, treats them
extensionally. See the 'direct semantics' (which is normative) for OWL-DL in
http://www.w3.org/TR/owl-semantics/direct.html, where the interpretation of a
class name is simply a subset of the universe. That is an extensional meaning
for classes. RDFS and the RDF-based semantics for OWL both distinguish between
the class itself I(<name>) and the class extension CEXT(I(<name>)), which
distinction allows for an intensional interpretation. (03)
Pat (04)
> 3. Classes
>
> Classes provide an abstraction mechanism for grouping resources with similar
>characteristics. Like RDF classes, every OWL class is associated with a set of
>individuals, called the class extension. The individuals in the class
>extension are called the instances of the class. A class has an intensional
>meaning (the underlying concept) which is related but not equal to its class
>extension. Thus, two classes may have the same class extension, but still be
>different classes.
>
> So, if "Classes are extensional" means two OWL 1 classes with the same extent
>are the same class, then clearly OWL 1 classes, while having extents, are not
>extensional - or else this paragraph in the OWL 1 LR is wrong. FWIW I checked
>the errata and this paragraph is not mentioned so it seems to stand as-is.
>
> The OWL 2 new features document claims "More importantly, backwards
>compatibility with OWL 1 is complete, both syntactically and semantically."
>even though I can't find any mention of the intensional meaning vs. class
>extension relationship in any of the OWL 2 documents. So what does Pat's
>"assumption of extensionality" mean wrt OWL 1 and OWL 2 and the question of
>whether two classes with the same extent are the same class?
>
> Cheers,
> David
>
>>
>> The "argument" given in the blog cited below is completely spurious: it is
>based on a common misunderstanding about model theory, that the individuals in
>models are "mathematical" entities rather than real things in the world, which
>is complete nonsense. It (the cited blog) also confuses extensionality with
>the idea of knowing or explicitly listing the elements of a set.
>>
>> Pat
>>
>>
>>> 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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