On Jul 8, 2012, at 2:30 PM, John F Sowa wrote: (01)
> On 7/8/2012 2:46 PM, Obrst, Leo J. wrote:
>> 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.
>
> I cannot believe that Peter Patel-Schneider and Ian Horrocks would make
> such an obvious blunder. Just look at their definitions:
>
> http://www.w3.org/TR/owl-semantics/direct.html (02)
Why is this a blunder? This is, as you yourself said earlier in the thread, the
normal textbook assumption about classes (ie properties, ie unary relations) in
classical model theory. And they certainly do make this assumption, in that
document. An abstract OWL interpretation maps class names to the powerset of a
universe of individuals (O, a subset of R, the denotation of owl:Thing) by a
map EC from V<sub>C, the set of class names, to P(O). Since the class *is* the
subset, two classes with the same members are the same class. (03)
>
>> 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).
>
> The question whether classes can be instances of classes is irrelevant.
> Common Logic allows relations to be arguments of relations. That option
> does not have the slightest effect on the distinction between intensions
> and extensions. (04)
True. (05)
>
> If the W3C had just adopted LBase semantics (and therefore CL model
> theory) all these questions would be completely clear. (06)
Well, I did manage to get the CL trick incorporated into the RDF/RDFS standard
and at least mentioned in the OWL standard (the last not without a huge fight,
ending in an awkward compromise.) And remember this was in 2003, four years
before CL was even published. (07)
> The people who
> try to replace logic with something "simpler" always create problems
> that are immensely more complex than anything they hoped to avoid.
>
> The W3C should have declared that anybody who could not pass a simple
> test on FOL would be disqualified from voting. Every professional group
> has minimum standards for membership *and* voting. You cannot allow
> incompetents to vote on technical issues. (08)
This would not have helped in the RDF/OWL case. the non-logicians were like
bystanders at a wrestling match. All the fighting was between the description
logicians, who know FOL as well as anyone, and, well, me. (09)
Pat (010)
>
> John
>
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> (011)
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