Charles,
Would it make sense to ask for the intersection of the extent of the type
"hat" and the set of things in my closet? I think so.
So at least the extent of the type would seem to participate in set
operations, making it a set.
So either a type HAS a set (extent) or it AS A set. If there is a "has
instance" relation directly from the type to instances then it would seem
that the type it's self is acting as the set.
If any number of assertions can be made to define a type, why is it so
strange that one form of such assertion would be an enumeration of the
instances of that type - essentially an enumerated type, this looks much
like a set.
So from either perspective it would seem there is some tie between type and
set. What would you suggest is that tie?
-Cory
> -----Original Message-----
> From: ontac-dev-bounces@xxxxxxxxxxxxxx [mailto:ontac-dev-
> bounces@xxxxxxxxxxxxxx] On Behalf Of Charles D Turnitsa
> Sent: Wednesday, February 01, 2006 7:09 PM
> To: ONTAC Taxonomy-Ontology Development Discussion
> Subject: RE: [ontac-dev] Representation of attributes
>
> I agree with Barry, although I may be wrong. :-) I believe that there is
> a big difference between Types and Sets.
>
> 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).
>
> 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.
>
> 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.
>
> Chuck
>
>
>
>
> ontac-dev-bounces@xxxxxxxxxxxxxx wrote on 02/01/2006 05:24:42 PM:
>
> >
> > > >
> > > > > 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
> >
>
>
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