SUO: Re: Foundation Ontology
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Robert,
Congratulations! This, at least, has some meat on it,
and I encourage you to put it through the SUO gauntlet.
Jon Awbrey
Robert E. Kent wrote:
>
> 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.html]. 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.html] 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
> Subj: 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
> > Subj: 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
> > Subj: 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
> > > Subj: 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
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