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Re: [ontolog-forum] Truth

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>, "Obrst, Leo J." <lobrst@xxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Sun, 8 Jul 2012 21:07:35 -0500
Message-id: <1ED95C9B-EF2C-4195-A544-43EE59AD1D20@xxxxxxx>

On Jul 8, 2012, at 1:46 PM, Obrst, Leo J. wrote:    (01)

> 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).     (02)

Close, but no cigar. Well, maybe a cheroot. First, planets arent classes, so 
the example is confusing. Let me use this instead. I have a class  TIT whose 
members are A, B and C, and another class TAT whose members are A and D, and 
someone proves that A=B and C=D. I can now conclude that TIT and TAT have the 
same members, are subclasses of one another, and are owl:EquivalentClass of 
each other, and various other things. Can I , however, conclude that TIT 
actually equals TAT, ie that TIT=TAT, or that TIT owl:sameAs TAT? Answer: no. 
You can't conclude that in OWL-Full because it doesn't follow: they might have 
the same members and still be distinct classes. They *might* be the same class: 
OWL-Full doesn't prohibit that, it just doesnt take a position one way or the 
other.     (03)

OWL-Full does allow classes to be instances, but this isnt the reason it is 
intensional. I confess to not being able to follow your last point above, but 
it sounds wrong.     (04)

As a matter of fact, you can't infer that TIT=TAT in OWL-DL either, but for an 
entirely different reason: OWL-DL syntax doesn't allow you to even pose the 
question. If it did, then the OWL-DL semantics do require that in this case, 
TIT and TAT are identically the same class.     (05)

Hope this helps.    (06)

Pat    (07)

> 
> 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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>     (08)

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40 South Alcaniz St.           (850)202 4416   office
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FL 32502                              (850)291 0667   mobile
phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes    (09)






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