Re: SUO: Ontology Structure & Content
----- Original Message -----
From: "John F. Sowa" <sowa@bestweb.net>
To: "Horn, Graham" <graham.horn@aihw.gov.au>; "'John F. Sowa'"
<sowa@bestweb.net>; "pat hayes" <phayes@ai.uwf.edu>; "West, Matthew MR
SSI-GREA-UK" <Matthew.R.West@is.shell.com>;
<standard-upper-ontology@majordomo.ieee.org>; "Awbrey Jon (E-mail)"
<jawbrey@oakland.edu>; "Fuchs E. Norbert (E-mail)" <fuchs@ifi.unizh.ch>;
"Whitten David (E-mail)" <whitten@lynx.eaze.net>
Sent: Saturday, January 13, 2001 9:23 AM
Subject: Re: SUO: Ontology Structure & Content
> The point I was making is that the lattice-based approach
> can support incremental modifications at any level of detail.
> I showed how Erdmann's original lattice, which I'm sure he
> would admit is very limited, can be extended by adding more
> distinctions to his table. Any or all of your distinctions
> can be incorporated in the lattice by makind additions and/or
> deletions one at a time (or two or three or more at a time,
> if you like). At every step of the way, you have a lattice,
> which can be automatically extended as far as you like.
It is important to review:
1. Any formal context (from Formal Concept Analysis) [instance set (formal
objects), type set (formal attributes), and incidence relation], or
equivalently classification (from Information Flow), automatically induces
an associated lattice, where the types and instances embed as "atomic"
lattice elements.
2. Any (generalized) theory (from Information Flow) [type set (formal
attributes), sequent-form constraints] induces a classification (formal
context), and vice-versa -- this is an adjoint situation.
3. Sums of formal contexts exist:
a. the sum of any two formal contexts exists [sum the types and product
the instances]
b. the apposition of any two formal contexts, which share the same set
of instances, exists (glues the formal contexts together along the type
dimension)
4. Sums of IF theories exist [sum the types, sum the constraints]
5. Sums of IF theories and classifications correspond. For more on this, see
the paper [http://www.ontologos.org/Papers/ISKO6/ISKO6.pdf].
6. The lattice induced by the sum (or apposition) is closely related to the
summand lattices
> The important point is to have a systematic methodology,
> preferably supported by software that can make the updates
> automatically. The techniques of Formal Concept Analysis
> are an example of such an approach, but there are other
> methods that can be used to supplement, extend, or even
> replace them as desired.
Summation (coproducting) is a basic construction in the category of
classifications (formal contexts). Another basic construction is
coquotienting, which can either represent type equivalencing or ontology
sharing. In either case, you end up with new categories that are equivalence
classes of old categories. These socalled colimiting constructions can be
done together. I wonder whether your techniques for supplementing, extending
and replacing are related to these colimiting constructions.
> Developing the tools and methodologies for extending, refining,
> and sharing ontologies are just as important, and perhaps even
> more important than any particular choice of categories we may
> develop or propose for the SUO.
Of course, I heartily endorse this position -- see the message
[http://ltsc.ieee.org/logs/suo/msg00371.html].
Robert E. Kent
rekent@ontologos.org