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Re: [ontolog-forum] Truth

To: Chris Mungall <cjmungall@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Sat, 7 Jul 2012 21:52:14 -0500
Message-id: <6E25F966-68D6-47F8-818E-CB5BFBADFA70@xxxxxxx>

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)
> 
> Regarding classes being the same as their extents in OWL: I don't think this 
>view is universally shared.    (02)

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.    (03)

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.    (04)

Pat    (05)


> 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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>     (06)

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phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes    (07)






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