Just thinking with my fingers on a keyboard: (01)
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), then, at least when representing Venus as a topic
(class) in a topic map, both are used as *scoped* names for that
object. 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. Not sure what to make of all this... (02)
Jack (03)
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
>>>>>>
>>>>>>
>>>>>> _________________________________________________________________
>>>>>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
>>>>>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
>>>>>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>>>>>> Shared Files: http://ontolog.cim3.net/file/
>>>>>> Community Wiki: http://ontolog.cim3.net/wiki/
>>>>>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>>>>>
>>>>> ------------------------------------------------------------
>>>>> IHMC (850)434 8903 or (650)494 3973
>>>>> 40 South Alcaniz St. (850)202 4416 office
>>>>> Pensacola (850)202 4440 fax
>>>>> FL 32502 (850)291 0667 mobile
>>>>> phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> _________________________________________________________________
>>>>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
>>>>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
>>>>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>>>>> Shared Files: http://ontolog.cim3.net/file/
>>>>> Community Wiki: http://ontolog.cim3.net/wiki/
>>>>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>>>>>
>>>>
>>>>
>>>> _________________________________________________________________
>>>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
>>>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
>>>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>>>> Shared Files: http://ontolog.cim3.net/file/
>>>> Community Wiki: http://ontolog.cim3.net/wiki/
>>>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>>>>
>>>>
>>>
>>> ------------------------------------------------------------
>>> IHMC (850)434 8903 or (650)494 3973
>>> 40 South Alcaniz St. (850)202 4416 office
>>> Pensacola (850)202 4440 fax
>>> FL 32502 (850)291 0667 mobile
>>> phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes
>>>
>>>
>>>
>>>
>>>
>>>
>>> _________________________________________________________________
>>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
>>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
>>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>>> Shared Files: http://ontolog.cim3.net/file/
>>> Community Wiki: http://ontolog.cim3.net/wiki/
>>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>>>
>>
>>
>> _________________________________________________________________
>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>> Shared Files: http://ontolog.cim3.net/file/
>> Community Wiki: http://ontolog.cim3.net/wiki/
>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>
> ------------------------------------------------------------
> IHMC (850)434 8903 or (650)494 3973
> 40 South Alcaniz St. (850)202 4416 office
> Pensacola (850)202 4440 fax
> FL 32502 (850)291 0667 mobile
> phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes
>
>
>
>
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> (04)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J (05)
|