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Re: [ontolog-forum] Truth

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "doug foxvog" <doug@xxxxxxxxxx>
Date: Wed, 11 Jul 2012 10:08:30 -0400
Message-id: <35a037096eabdbfb3a84996ec9cc4cf2.squirrel@xxxxxxxxxxxxxxxxx>
On Tue, July 10, 2012 14:29, Pat Hayes wrote:>
> On Jul 10, 2012, at 12:56 PM, doug foxvog wrote:
>> On Sun, July 8, 2012 22:11, Pat Hayes wrote:
>>> On Jul 8, 2012, at 3:41 PM, Jack Park wrote:
>> ...
>>>> , both [MorningStar and EveningStar] are used as *scoped*
>>>> names for that object.    (01)

>>> I have no idea what ypou mean by a scoped name.    (02)

>> It seems to me that he means that in certain contexts that name
>> refers to that object, but in others it does not.    (03)

> But there are no "contexts" in RDF or OWL or Common Logic, for that
> matter. So I repeat, I have no idea what he means.    (04)

Common Logic does not ban contexts.  In RDF, one could consider the graph
in which a statement appears to be its context.    (05)

OWL is such a limited language that it is unable to implement contexts.    (06)

>>> Names in the RDF language family are IRIs, so have no local scope.    (07)

>> The scope (context) is not for the name, but for the name being a
>> referent for a specific object.    (08)

> The whole idea of URIs is that they are universal, ie they do not refer
> differently in different contexts. That is what they are FOR.    (09)

Pat, you signed off in the middle of a paragraph just before the example
i provided!    (010)

Do the URIs  .../PresidentOfIreland and .../KingOfNorway refer to the
same thing in every context?  Or would you disallow such URIs for
individuals?  Would you require them (like EveningStar and MorningStar)
to represent classes that could have one instance at one time, another
instance at another time, and no instances at still other times?    (011)

-- doug    (012)

> Pat    (013)

>> You certainly aren't suggesting that
>> RDF can not have IRIs such as .../PresidentOfIreland or
>> .../KingOfNorway.    (014)

>> -- doug f
>>>> 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.
>>> AFAIK, there are no scoped labels or names in any OWL dialect.
>>>> Not sure what to make of all this...
>>> I dont think scoping has anything at all to do with the
>>> extensional/intensional distinction.
>>> Pat
>>>> 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
>>>>> 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:
>>>>>>>>>> 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?    (015)

>>>>>>>>>> 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.    (016)

>>>>>>>>>> http://www.w3.org/TR/rdf-mt/#sinterp    (017)

>>>>>>>>>> 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.    (018)

>>>>>>>>>> Pat will probably jump in here and straighten me out...    (019)

>>>>>>>>> (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    (020)

>>>>>> 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    (021)

>>>>>>> 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    (022)

>>>>>>>> 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    (023)

>>>>>>>>>> -chris    (024)

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