I agree with Barry, although I may be wrong. :-) I believe that there is
a big difference between Types and Sets. (01)
Types are suggested by the inherent categorization of the ontology (whether
that is natural order, in the case of biological domains, or based on form
or function in man-made domains, or whatever - it is some sort of ordering
suggested by the domain the ontology seeks to represent). (02)
Sets, on the other hand, are ad hoc collections of things. A formal
definition (suggested by set theory) might be "any collection of distinct
things thought of as a whole". It may be based on defining rules , or it
may be completely arbitrary. It may assist the user of the an ontology,
but I don't see it as being part of an ontology's categorization of its
entities. (03)
I still think that there is a third categorization group, what I call
Classes, that have to do with satisfying rulesets that are external to the
ontology, but I haven't formulated my thoughts here yet. The sorts of
rulesets that I am thinking of, however, might be something like Whitehead
(or, more modernly, Sowa's) categorization labels, or perhaps the
categories from a grammar. As I said, I'm still working on it, but it
seems somewhat obvious that there is a third group of categories that are
not Types, and yet not so loose as what I define as Sets. (04)
Chuck (05)
ontac-dev-bounces@xxxxxxxxxxxxxx wrote on 02/01/2006 05:24:42 PM: (06)
>
> > >
> > > > MW: That sounds reasonable, but we still need something more
general
> > > > that says "here are some things" in an abstract way.
>
> how about: "here are some things"
>
> or better still: "here are some entities"
> > >
> > > [cbc] That, to me, is type. We can attach intentional
> > > statements to it or
> > > an extension to it. It is then the instance and subtype
> > > relations that make
> > > "type" interesting and well defined.
> > > One way to define a type is to make rules, another way is to
enumerate
> > > instances. In this sense "set" is a subtype of "type".
> >
> >MW: If that includes {my right ear, the moon, rabbit} then I would be
> >entirely happy. But that is not what I am hearing from others.
>
> If set is a subtype of type, and
>
> {my right ear, the moon, rabbit} is a set
>
> then
>
> {my right ear, the moon, rabbit} is a type.
>
> Someone should teach Matthew, one day, about what is called a
> reductio ad absurdum argument.
> BS
> (07)
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