Re: SUO: Re: IFF Comments Requested
Pat,
Comments below.
Pat Hayes wrote:
>
> > ATTN SUO Voting Members,
> >
> > For those who don't subscribe or perhaps filter messages
> > from the
> > SUO list, please take special note of this formal request for
> > comments on
> > the IFF document.
> >
> > SUO voting rules require members to participate, though this
> > has
> > never been specifically defined. For those who don't participate in
> > content
> > discussions, this call for comments is an excellent opportunity to
> > contribute to the work of this group.
> >
> > Jim Schoening
> > Chair
> >
> > -----Original Message-----
> > From: Jim Farrugia [mailto:jim@spatial.maine.edu]
> > Sent: Thursday, October 04, 2001 2:46 PM
>
> > To: standard-upper-ontology@ieee.org
> > Cc: Jim Farrugia
> > Subject: SUO: IFF Comments Requested
> >
> >
> > ATTN SUO WG,
> >
> > It is now time for active SUO members to do a thorough review of
>
> > IFF.
>
> There doesn't yet seem to be anything to review.
>
> > The vote on IFF was only to decide whether to commence work on it,
>
> > not to decide what changes or improvements to make. But we are now
> > requesting that members review the IFF and submit suggested
> > changes.
> >
> > The IFF now lives in extended form at http://suo.ieee.org/IFF.
> > It consists of four pieces: an Introduction, a Core subOntology,
> > a Category Theory subOntology, and a Classification subOntology.
>
> None of those Ontologies can be accessed from that URI.
>
> >
> > We have also posted a "changes.htm" file
> > (http://suo.ieee.org/IFF/changes.htm)
> > that describes the differences between the starter document and the
> > extended version that now exists. (Essentially, some sections that
> > were
> > only sketched out in the starter document are now more fully fleshed
> > out
> > into separate pieces. The exception is that the model theory section
> > of
> > the starter document has not yet been made into its own separate
> > document.)
> >
> > Please submit your comments by October 18, 2001, replying to this
> > subject line ("IFF Comments Requested"), so that we can easily
> > gather all
> > comments. (At some point later, we may suggest other subject lines
> > to
> > group together related comments.)
>
> OK, I have a few.
>
> First, I fail to see the utility of the emphasis placed on category
> theory. This is not motivated anywhere, but it badly needs to be
> motivated if you expect anyone to take it seriously enough to even
> read the sources to find out what you are talking about.
>
I agree the motivation is missing from the document. I do think there is
a motivation. I hope to add to it incrementally.
> Second, I do not understand what the intended role of the KIF axioms
> is to the rest of the proposal; there seems to be no connection
> between the contents of the KIF structural ontology and topos theory.
> In particular, I simply cannot make sense of the 'categorical
> property'. What new-KIF are you talking about, that is entirely
> category-theoretic?
>
Bob can probably answer this better.
> Third, the comment: "This foundational approach should answer Solomon
> Feferman's qualms about logical and psychological priority" seems to
> me to be particularly unfortunate, since it manifestly does *not*
> answer them. Now, I would be inclined to suggest that proper classes,
> small sets, etc etc, and all the other post-Russellian FOM concerns
> that suffuse topos metatheory in fact have virtually no relevance to
> an upper ontology in any case, and are best simply put aside as
> irrelevant (or only marginally relevant); but since you apparently do
> not want to take this easy way out of the kitchen, you had better be
> ready to take some heat.
>
I think Bob here is just bringing to mind what seems to him to be
relevant notions. I agree that they are not relevant to us and our task.
> Fourth, you seem to have been misled by a pun on the word "class". As
> used in KIF and throughout the DL logic literature (and indeed the OOP
> and database communities), this does NOT mean 'proper class' in the
> sense used in topos theory. In fact, KIFclasses constitute a(n
> extremely small) sub-collection of the sets; every KIFclass
> (extension) is a set, but not all sets are KIFclasses. (A trivial
> consequence of the completeness theorem.) Proper classes, in the topos
> sense, are not even in the domain of discourse. So to interpret
> KIF:Class as meaning conglomerates in the Adamek, Herrlich & Strecker
> sense is just plain silly. (BTW, what a *terrible* choice as a guiding
> text. This is like watching someone commit ritual suicide. Do you
> seriously expect a sizeable number of IEEE members to read such a
> book? You could at least have cited a slightly readable intro, such as
> 'categories for the working mathematician'.)
>
Again, my previous comment holds: Bob probably goes beyond our relevance
here.
> Fifth, in spite of the reference to McLarty, there is something highly
> suspicious in claiming to give a first-order axiomatization of any
> part of topos theory, in view of the fact that first-order logic
> satisfies the compactness and completeness theorems with respect to a
> model theory based on sets. Evidently, one doesn't need the proper
> classes in order to explain topos, then, right? In fact, that entire
> conglomerate diagram can all just be dismissed as fantasy, if those
> really are first-order logic axioms. (Or did you have some kind of
> nonstandard models in mind, perhaps? So what model theory are you
> assuming for your first-order axioms, maybe you could tell us?) This
> is really a very hot kitchen, and I am going to hold your hands over
> the fire until you squeal.
>
> 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.
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. 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.
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.
Leo
>
> Pat Hayes
>
> PS. There already is a semantics for DAML+OIL, by the way. You can
> find it on the DAML+OIL website. Peter Patel-Schneider, the author, is
> currently revising it to bring it into line with the model theory for
> RDF(S).
>
> --
>
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Dr. Leo Obrst The MITRE Corporation
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