Pat, (01)
Comments below. (02)
Thanks,
Leo (03)
-----Original Message-----
From: Pat Hayes [mailto:phayes@xxxxxxx]
Sent: Sunday, July 08, 2012 10:08 PM
To: [ontolog-forum] ; Obrst, Leo J.
Cc: David Price
Subject: Re: [ontolog-forum] Truth (04)
On Jul 8, 2012, at 1:46 PM, Obrst, Leo J. wrote: (05)
> 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). (06)
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.
[Leo: ] Yes, that's a more realistic example. (07)
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.
[Leo: ] I thought you were saying that the fact that OWL-Full allows classes to
be instances was why OWL-Full was intensional. It didn't exactly make sense to
me, and so I was trying to understand it by contriving something. Or Motik
(2005) [1] uses the example "a(a)", where the symbol 'a' is used as both
concept and individual. However, personally, I don't think this meta-modeling
issue (class and instance) makes OWL-Full intensional, but I wonder what does. (08)
[Leo:] But I think part of the problem is in Section 3 of the OWL Language
Reference that David brought up, i.e., http://www.w3.org/TR/owl-ref/#Class: (09)
"3. Classes (010)
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. (011)
When in this document we use wording such as "a class of individuals ..", this
should be read as "a class with a class extension containing individuals ...". (012)
NOTE: In OWL Lite and OWL DL an individual can never be at the same time a
class: classes and individuals form disjoint domains (as do properties and data
values). OWL Full allows the freedom of RDF Schema: a class may act as an
instance of another (meta)class. (013)
OWL classes are described through "class descriptions", which can be combined
into "class axioms". We first describe class descriptions and subsequently turn
to class axioms. "
[Leo:] From the above, it sounds like all of OWL is intensional, not just
OWL-Full, which is more in line with how description logics have been generally
portrayed before, i.e., with the Tbox constructs of concept and role being
intensional, and the Abox being extensional. Perhaps this is more of a
"colloquial" use of "intension" and "extension", as in intensional database
(schema) vs. extensional database (rows), rather than being a formal
intensional or extensional semantics? But my question remains: what makes
OWL-Full intensional? (014)
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. (015)
Hope this helps. (016)
Pat (017)
[Leo: ]
Motik, Boris. 2005. On the Properties of Metamodeling in OWL. In: 4th Int.
Semantic Web Conf. (ISWC 2005).
http://dip.semanticweb.org/documents/Boris-Motik-On-the-Properties-of-Metamodeling-in-OWL.pdf.
>
> 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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