Dear Mike, (01)
> I see that the OWL 2 spec states that "/Classes/ can be understood as
> sets of individuals."
>
> I seem to recall that in OWL1, a Class could be understood both as
> extensional (a set of individuals) and intensional (a class has a
> collection of properties which would define the members of the set,
> i.e.
> all individuals which have those properties are seen as members of that
> set - so still effectively a set of individuals, but arived at
> differently).
>
> Am I right in assuming that the existence of properties and axioms
> provides for intensional definition of classes, so that OWL2 supports
> both? I guess I'm stating the obvious there, and the document on
> semantics would seem to bear this out. However, that does mean that OWL
> Class maps to both intensional Type and extensional Set. Or am I
> missing
> something? (02)
[MW] It depends. (03)
If I ask you "How many humans are there?" and your answer is in the order of
6.7 billion, and a few years later I ask the same question and you say 6.8
billion, then you were not talking about a set. (04)
On the other hand, if your response is that you can't tell me that, but that
the set alive today is 6.7 billion, but that the set of all humans includes
all those that have lived and all those yet to live, and you can't give a
number for that - then you are talking about sets. (05)
Regards (06)
Matthew West
Information Junction
Tel: +44 560 302 3685
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matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.matthew-west.org.uk/ (07)
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>
> Mike
>
> John F. Sowa wrote:
> > Dick,
> >
> > RHM> I finally understand that Class is the extension set of Concept.
> > > Now, all of the "strange" properties of "Class" are obvious,
> because
> > > "Class" is just a set.
> >
> > The word 'class' has created an enormous amount of confusion in
> computer
> > all branches of computer science and related subjects. The problem
> is
> > caused by three very different definitions of the word:
> >
> > 1. Cantor used the word 'Menge', which some people translated to
> > English as 'set' and others as 'class'. Therefore, many people
> > still use the two English words as synonymous.
> >
> > 2. As a result of the paradox of all sets that are not members of
> > themselves, logicians have used the word 'class' as a supertype
> > that includes sets and other collections that are "too big" to
> > obey all the usual axioms of set theory.
> >
> > 3. In object-oriented programming systems, people have adopted the
> > word 'class' as a synonym for 'type'. That is an extremely
> > unfortunate choice of word that should be outlawed. It creates
> > an immense amount of confusion without any redeeming social
> value.
> >
> > The distinction between intension and extension is critical.
> > The word 'type' has been well established in English and other
> > natural languages for distinguishing different kinds of entities
> > by their definitions, not by the sets of existing entities.
> > It is also widely used in programming languages and systems for
> > entities distinguished by their definitions, independently of
> > the sets of existing things of those types.
> >
> > Since none of the sets used in computer science are so big that we
> > have to use the word 'class', there is no reason for anyone to use
> > the word 'class' in anything that has to do with computer systems.
> >
> > Therefore, I suggest that we use two words: 'set' for the extensional
> > meaning, and 'type' for the intensional. The word 'class' in O-O
> > systems should be replaced by 'type'. I realize that it is an uphill
> > battle to get people to change the terminology of their programming
> > languages. But I would use the pair of terms 'set' and 'type' for
> > all metalevel discussions about such languages and systems.
> >
> > It is truly unfortunate that OWL has adopted the word 'class'
> > instead of 'type'. However, that is not the only truly unfortunate
> > aspect of OWL. I don't believe that the world should perpetuate
> > the decisions frozen into OWL.
> >
> > John Sowa
> >
> >
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>
>
> --
> Mike Bennett
> Director
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