RE: SUO: Re: IFF Comments Requested
Dear Pat and Leo,
Since my name was taken in vain below, I'll add my two cents worth.
Matthew West
Principal Consultant
Shell Information Technology International Limited
Shell Centre, London SE1 7NA, United Kingdom
Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
Email: matthew.r.west@is.shell.com
Internet: http://www.shell.com
> -----Original Message-----
> From: Pat Hayes [mailto:phayes@ai.uwf.edu]
> Sent: 10 October 2001 17:44
> To: Leo Obrst
> Cc: standard-upper-ontology@ieee.org
> Subject: Re: SUO: Re: IFF Comments Requested
>
>
>
> > >
> >> Sixth. Let me back off from having FOM fun with y'all and
> get to the
> >> main point. The purpose of ontologies is to represent facts about
> >> worlds, not to play elegant games in the foundations of
> mathematics.
> >> Matthew West wants to describe oil flowing along
> pipelines, that kind
> >> of thing. Now, what connection, even of the most remote
> kind, can you
> >> suggest there is going to be between ANY such activity of
> describing
> >> the real world, and ANY of this mathematical gamesmanship of topos
> >> theory? So far, I can't see any.
MW: Well the same could be said of set theory, though I am quite
convinced it is very important.
MW: I am actually quite concerned that what we develop has firm
foundations, and that we are not squeezing the real world to try
to make it fit "convenient" mathematical theories. This is why
I am very pleased with the work Chris M has done in proposing
a set theory that does not impose constraints that make problem
solution convenient, but require some bits of reality to be ignored.
MW: One of the things I have been finding unsatisifactory is the
concept of a relation, and over the last few years I've been looking
at this with others to try to understand what we mean when we use that
construct. Interestingly, when I now start to read about Category
Theory, I find a very good correspondance with where that was going.
So I think it likely that Category Theory has a proper place.
> >
> >I think you are wrong, here, Pat. No, we are not here to play
> >mathematical games, but really do have pragmatic concerns
> just exactly
> >like Matt does.
>
> I'm sure you are: I didn't mean to criticize your motives,
> only your document.
MW: Well yes it is an early draft so expectations should be low.
Still it is criticism that is the fire of improvement.
>
> >However, we do need to build a framework which enables
> >us to cobble together different ontologies (theories) in a reasonable
> >fashion and perhaps even a framework to enable us to
> "compose" theories,
> >i.e., to be able to "place" theories in an overarching framework and
> >then link or (God help us) even "project" those theories'
> >"intersections". If we don't do this, who will? Personally, I think
> >category theory will help.
MW: Well actually I am fairly certain you can do this with Set Theory
(at least the one Chris M has proposed) and FOL.
However, I give other arguments for category theory above.
>
> Ah, now THAT does make sense. BUt this seems to be quite a different
> theme than the one in the IFF document. What you are saying here is
> that the category theory can provide a framework for a kind of
> structural meta-theory of ontologies; for talking about structural
> relationships between ontologies, as is done in the SpecWare system
> also. That isn't what the IFF seems to be saying at all, though: it
> is talking about categories being the *subject-matter* of ontologies.
> For example, your picture of categories in the structural meta-theory
> is quite compatible with the ontologies themselves being written in,
> say, DAML and being about, say, states of viscosity of different
> grades of crude oil.
>
> >
> >I intend to discuss your issues a bit further (and later),
> since I don't
> >see any incongruity between the "logic" view and the
> "category theory"
> >view. The category theory view is simply more general.
>
> Well, if so, I'm tempted to ask, why is FOL offered as the basic
> axiomatization of topos theory for foundational reasons in the IFF
> document?
>
> Pat
> --
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