On Jul 8, 2012, at 3:41 PM, Jack Park wrote: (01)
> Just thinking with my fingers on a keyboard:
>
> It seems to me that if "MorningStar" is the name given to Venus when
> it is visible in the morning
> (http://en.wikipedia.org/wiki/Morning_Star) and if "EveningStar" is
> the name given to Venus when visible in the evening (linked from same
> Wikipedia entry), (02)
OK so far. (03)
> then, at least when representing Venus as a topic
> (class) in a topic map (04)
AFAIK, topic maps have no coherent semantics, but it seems very odd to say that
a planet is a class. While not strictly illegal in OWL-Full, this would be very
bad ontology design (and it is illegal in OWL-DL). (05)
> , both are used as *scoped* names for that
> object. (06)
I have no idea what ypou mean by a scoped name. Names in the RDF language
family are IRIs, so have no local scope. (07)
> It's confusing, I suppose, that topic maps use the term
> "name" for what is known as "label" in OWL, and not for the URI
> (identifier) of the object. I don't recall reading about scoped
> labels in OWL. (08)
AFAIK, there are no scoped labels or names in any OWL dialect. (09)
> Not sure what to make of all this... (010)
I dont think scoping has anything at all to do with the extensional/intensional
distinction. (011)
Pat (012)
>
> Jack
>
> On Sun, Jul 8, 2012 at 11:46 AM, Obrst, Leo J. <lobrst@xxxxxxxxx> wrote:
>> Pat,
>>
>> So if I understand your statements correctly, two OWL classes EveningStar
>and MorningStar will be equal if their extensions are the same, i.e., {venus},
>or:
>> EveningStar = MorningStar. And that this holds of OWL-DL, but not of
>OWL-Full, correct? In OWL-Full, EveningStar \= MorningStar, even if they have
>the same extension (apparently because OWL-Full allows classes to be
>instances, and that therefore, one does not know if the extension of a given
>class includes the instance or the class).
>>
>> Thanks,
>> Leo
>>
>> -----Original Message-----
>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
>> Sent: Sunday, July 08, 2012 11:12 AM
>> To: [ontolog-forum] ; David Price
>> Subject: Re: [ontolog-forum] Truth
>>
>>
>> On Jul 8, 2012, at 8:34 AM, David Price wrote:
>>
>>>
>>> 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:
>>
>> 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.
>>
>> Pat
>>
>>
>>> 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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