Types have extensions, which are sets.
Not all sets are extensions of types.
BS (01)
At 01:39 AM 2/2/2006, you wrote:
>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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