SUO: Re: RE: Re: Foundation Ontology
Hi Matthew,
At first glance it seems reasonable, but I would want to look at the
details. And whatever the outcome, I think it is important that we keep a
complete distinction and an explicit boundary between the object level and
the metalevel. This fundamental partition should be obviously manifest in
the SUO. Some ontologies at the object level may choose to represent
metalevel concepts, but they would still be doing so at the object level.
Robert E. Kent
rekent@ontologos.org
----- Original Message -----
From: "West, Matthew MR SSI-GREA-UK" <Matthew.R.West@is.shell.com>
To: "SUO" <standard-upper-ontology@ieee.org>
Sent: Wednesday, May 23, 2001 4:56 AM
Subject: SUO: RE: Re: Foundation Ontology
>
> Dear Robert,
>
> I am also thinking of submitting the EPISTLE Core Model
> (as a start point for reference 4D ontology) and
> the IIDEAS Architecture (as an architecture and methodology
> for mapping/integrating different ontologies) as parts of what
> we need.
>
> I think that the work that Chris Menzel has done, and what
> you are proposing may fit as a layer above the EPISTLE Core
> Model. Does that make sense to you?
>
> Regards
> Matthew
> ===============================================================
> Matthew West http://www.matthew-west.org.uk/
>
> Principal Consultant Shell Visiting Professor
> Operations & Asset Management The Keyworth Institute
> Shell Services International The University of Leeds
> http://www.shellservices.com/ http://www.keyworth.leeds.ac.uk/
>
> H3229, Shell Centre, London, SE1 7NA, UK.
> Tel: +44 207 934 4490 Fax: 7929 Mobile: +44 7796 336538
> ===============================================================
>
> > -----Original Message-----
> > From: Robert E. Kent [mailto:rekent@ontologos.org]
> > Sent: 22 May 2001 19:31
> > To: Schoening, James R CECOM DCSC4I
> > Cc: SUO
> > Subject: SUO: Re: Foundation Ontology
> >
> >
> >
> > Jim,
> >
> > Yes, I have been thinking about submitting the Foundation
> > Ontology, but it
> > looks like I need a couple more weeks. In the discussion
> > below, I give an
> > overall picture of the ontological framework that I envision,
> > I discuss some
> > of the conceptual problems being addressed, and I suggest a
> > path for review
> > and editing. Because of my expanded response, I am cc-ing
> > this to the list
> > at large.
> >
> > ____________________
> >
> > The *overall picture* I have for an "industrial strength" ontological
> > framework goes is follows:
> >
> > 1. There is a basic or core IFF ontology that interfaces the
> > new KIF logical
> > language with the metalevel ontological framework. This would
> > be close to
> > that expressed as Chris Menzel's Basic Ontology, but perhaps
> > a bit simpler
> > since only a few things are needed -- class, subclass,
> > function, signature,
> > pairing '[-]', and projections '(- 1)', '(- 2)' etc.
> >
> > 2. There is a (rather large) metalevel (= structural level)
> > ontology that
> > breaks up into two essential parts corresponding to the large/small
> > distinction in set-theoretic and category-theoretic foundations.
> >
> > 2.1 The upper metalevel represents the "large" notion of
> > foundations. This
> > is where the Foundation Ontology resides; the other
> > components in this upper
> > metalevel are the Category Theory Ontology and the large
> > Classification &
> > Concept Lattice Ontology, the latter allowing us to represent
> > the *truth
> > classification* and *truth concept lattice*, an overall goal for this
> > effort. The Foundation Ontology essentially represents
> > set-theoretic classes
> > and their functions -- thus modeling the "large" notion of
> > foundations.
> >
> > 2.2 The lower metalevel represents the "small" notion of
> > foundations. A
> > specific goal of the lower metalevel is to represent some
> > central notions of
> > model theory -- models (first-order structures), expressions and
> > satisfaction. In the approach that I am suggesting, models
> > are 2-dimensional
> > structures composed of small classifications along one
> > dimension and small
> > hypergraphs (or spans) along the other; here classifications
> > represent the
> > instance-type distinction, whereas hypergraphs represent the
> > entity-relation
> > distinction. The lower metalevel makes heavy use of the upper
> > metalevel --
> > indeed, a goal in modeling the lower metalevel is to abide by the
> > CATEGORICAL PROPERTY (see
> > [http://suo.ieee.org/ontology/msg02399.html]).
> >
> > 3. The object level is where the content ontologies reside.
> > These could be
> > very generic, such as a 4D ontology, or specific, such as
> > ontologies for
> > government or higher education. It should be noted that the
> > object level
> > satisfies a representation property similar to the
> > categorical property
> > satisfied by the lower metalevel -- the ontological language
> > used is not
> > KIF; instead it is the terminology defined and axiomatized in
> > the lower
> > metalevel (terms such as 'subtype', 'instance', 'expression', 'model',
> > 'ontology', 'relation', 'entity', 'role', etc.).
> >
> > ____________________
> >
> > Here is a discussion of some of the *conceptual problems*
> > being addressed:
> >
> > One reason for the delay in submitting the Foundation Ontology is the
> > following. Initially, I had thought that the Foundation
> > Ontology, which as I
> > mentioned above models set-theoretic classes and their
> > functions, would
> > encode the axioms for a *Cartesian-closed category* (and that the Set
> > Ontology, which models small sets and their functions, would
> > encode the
> > axioms for a *topos*). To test this I was using lower
> > metalevel ontologies,
> > such as the Classification Ontology. But recently, in order
> > to satisfy the
> > categorical property, I seemed to need "power classes" (see
> > [http://suo.ieee.org/ontology/msg02381.html]) in order to
> > represent some
> > aspect of fibrations (specifically, the category of
> > classifications and
> > infomorphisms is fibered over the category of sets and
> > function along the
> > "instance functor"). See McLarty's suggestion to use
> > Benabou's theory of
> > fibrations and definability
> > [http://www.risc.uni-linz.ac.at/research/category/risc/catlist
> > /goedel-cat].
> > My current belief is that fibers can be represented in the Foundation
> > Ontology, without a full-blown representation of fibrations a
> > la Benabou. In
> > order to do this however, we seem to require that the
> > Foundation Ontology
> > encode the axioms for a *topos* (see McLarty's first order
> > expression of the
> > theory of a well-pointed topos with natural numbers and choice
> > [http://www.math.psu.edu/simpson/fom/postings/9802/msg00072.ht
> > ml]. These
> > axioms are now incorporated in the Foundation Ontology.
> > Perhaps this version
> > of the Foundation Ontology would partially satisfy Feferman's
> > representational needs, as expressed in the FOM list
> > Toposy-turvey thread
> > [http://www.math.psu.edu/simpson/fom/postings/9801/msg00164.html].
> >
> > ____________________
> >
> > Here is one possible *path for review* and edit of the
> > Foundation Ontology:
> >
> > A. Submit to the SUO list for review, comments and criticisms. Beyond
> > set-theoretic critiques, also needed are comments about the
> > new KIF and
> > concepts used from Chris Menzel's Basic Ontology.
> >
> > B. Ask a select number of category-theorists to review. I
> > have in mind the
> > following people:
> > - Ross Street [http://www.maths.mq.edu.au/~street/], a
> > category-theorist
> > who seems to have some interest in applications (see his link
> > to Category
> > Theory at The Boeing Company, which refers to the Specware software
> > mentioned by Michael Uschold
> > [http://suo.ieee.org/ontology/msg00375.html]);
> > - Colin McLarty
> > [http://www.cwru.edu/artsci/phil/mclarty.html], who gave
> > the challenge topos axioms mentioned above, and has written a
> > topos-theory
> > book "Elementary Categories, Elementary Toposes"
> > [http://www.oup-usa.org./docs/0198514735.html];
> > - Bill Lawvere [http://www.acsu.buffalo.edu/~wlawvere/],
> > who is one of
> > the primary creators of topos theory, and whose interest in
> > applications
> > (although a theorist) is indicated in the very detailed response
> > [http://merwan.sunyerie.edu/~alsani/ctmail01-04,01/msg00014.ht
> > ml] that he
> > gave to a question of Mike Healy's on the category list.
> >
> > C. Submit to the category list at large for review, comments
> > and criticisms.
> >
> > ____________________
> >
> > Robert E. Kent
> > rekent@ontologos.org
> >
> >
> >
> > ----- Original Message -----
> > From: "Schoening, James R CECOM DCSC4I"
> > <James.Schoening@mail1.monmouth.army.mil>
> > To: "'Robert E. Kent'" <rekent@ontologos.org>
> > Sent: Monday, May 21, 2001 3:00 PM
> > Subject: RE: Foundation Ontology
> >
> >
> > > Robert,
> > >
> > > Any further thought of submitting the Foundation Ontology as a
> > > starter document in SUO? As you know, the group needs one or more
> > documents
> > > to focus its efforts on.
> > >
> > > Jim Schoening
> > >
> > > -----Original Message-----
> > > From: Robert E. Kent [mailto:rekent@ontologos.org]
> > > Sent: Thursday, March 08, 2001 1:44 PM
> > > To: Schoening, James R CECOM DCSC4I
> > > Subject: Re: Foundation Ontology
> > >
> > >
> > > Jim,
> > >
> > > Possibly eventually -- not for merger with Ian's effort, but as an
> > > alternative approach. However, the IFF Foundation Ontology
> > is still being
> > > worked on, with much feedback from several of the other IFF
> > ontologies
> > such
> > > as Spans, Categories, Sets and Classifications (there is a lot of
> > synergism
> > > taking place right now). Although the fundamental idea is
> > reasonably firm,
> > > the KIF code (at the ontologos site
> > [http://www.ontologos.org/IFF/IFF.html])
> > > is still in a flux. Perhaps in a month or so it will stabilize.
> > >
> > > Robert E. Kent
> > > rekent@ontologos.org
> > >
> > > ----- Original Message -----
> > > From: "Schoening, James R CECOM DCSC4I"
> > > <James.Schoening@mail1.monmouth.army.mil>
> > > To: "'Robert E. Kent'" <rekent@ontologos.org>
> > > Sent: Sunday, February 25, 2001 7:26 AM
> > > Subject: RE: Foundation Ontology
> > >
> > >
> > > > Robert,
> > > >
> > > > I forget if I've already asked you this.
> > > >
> > > > Is this Foundation Ontology something the SUO WG could use as a
> > > > starting point to develop a completed SUO document? If
> > so, would you
> > like
> > > > to discuss the option of submitting this as a starter
> > document. If so,
> > > > let's discuss some more.
> > > >
> > > > Jim
> > > >
> > > > -----Original Message-----
> > > > From: Robert E. Kent [mailto:rekent@ontologos.org]
> > > > Sent: Tuesday, February 20, 2001 5:09 PM
> > > > To: SUO
> > > > Subject: SUO: Foundation Ontology
> > > >
> > > >
> > > > All,
> > > >
> > > > I am working on a Foundation Ontology. I would appreciate
> > any comments
> > and
> > > > criticisms. This is located at:
> > > >
> > > > http://www.ontologos.org/IFF/Metalevel/Foundation%20Ontology.pdf
> > > >
> > > > Robert E. Kent
> > > > rekent@ontologos.org
> > > >
> >
>