Hi Pat (and group); (01)
My focus at work happens to be more fine-grained than the partial
ordering of theories. (02)
But, perhaps there is no disagreement, because I claim that any partial
ordering of theories must either be (i) declared by fiat (like
ontolingua's "uses" relation or Cyc's "genlMt" relation; or (ii)
determined by a complete reconciliatory mapping between potentially all
axioms of the respective theories. Declarative partial ordering
presupposes that the two theories are already consistent with one
another where one theory is "using" the other and where both theories
share a common content model and meta-model. (03)
I claim that the theories that "use" one another must be "consistent",
abide by a common model and, therefore, don't need to be mapped to
another. But I claim that such a endeavor (the reconciliation of
already reconciled theories) is less relevant to this group. If that is
true, we must determine partial ordering of theories by first
mapping/reconciling their respective axioms. (04)
Because my customer started with a DOLCE-derived artifact, our ontology
lacks the depth and breadth of some of the larger ontologies. (05)
I claim that our work must have near-term relevance. And for this
group's work to be directly relevant to my customer, we would need to
make sure that any creation of a lattice of theories is focused on the
mapping of pairs of axioms to one another - in such a way as to "grow" a
larger effective ontology. (06)
For us, this means grafting (via mapping) subtrees of key content into
DOLCE from other ontologies. I'm happy to view this a part of a larger
n^2 everything-to-everything mapping. I say n^2 because no one voiced
agreement with my proposal to agree on mapping to a single hub ontology
starting point. (07)
By making such fine-grained mappings we will be contributing to the
partial ordering of theories by mapping individual axioms to one
another. Only after such mapping, I claim, is partial ordering of
theories embodying differing models possible. (08)
Best, (09)
-Eric (010)
> -----Original Message-----
> From: ontac-forum-bounces@xxxxxxxxxxxxxx
[mailto:ontac-forum-
> bounces@xxxxxxxxxxxxxx] On Behalf Of Cassidy, Patrick J.
> Sent: Tuesday, November 01, 2005 10:31 AM
> To: ONTAC-WG General Discussion
> Subject: RE: [ontac-forum] Surveyed Ontology "Library"
Systems -
> - parts
>
> John's outline is, I think, a good clear summary of the
general
> goals
> that I also believe this group can make progress toward. I
> would just
> add one additional point:
>
> Since interoperability of different systems will hinge on
the
> clear
> specification of how their conceptual models are related, a
> registry
> that will serve for our purposes should have built-in
mechanisms
> for
> specifying at some level of detail how different ontologies
> relate to
> each other. At the lowest level, no analysis may have been
made
> to
> determine how one ontology relates to others in the
registry,
> and it
> will stand on its own in isolation. At another level, a
domain
> ontology may have been built explicitly to be defined by and
to
> conform
> to the theories in some upper ontology in the registry.
There
> can be
> partial alignment as well, and some method would be helpful
to
> specify
> in a usable way how the ontologies in the registry relate to
> each
> other; two domain ontologies, for example, may be logically
> consistent
> except with respect to some restricted uses in a particular
> context.
> Dagobert Soergel has taken the initiative to begin
organizing
> the
> ONTACWG subgroup that will study what our requirements are
for
> registries, so that we can make recommendations to the
groups
> that are
> actually building registry systems. He will be sending a
note
> to the
> list soon.
> The important distinction between the proposed Common
> Semantic Model
> and a simple registry of ontologies is that to be a
component of
> the
> COSMO, the logical relations of a theory must be specified
> clearly, in
> the manner John describes, or perhaps some other at least as
> precise,
> to the others in the COSMO, so that the relations between
> concepts in
> different theories, and particularly identity, will be
> recognizable and
> usable for automated reasoning.
> This does not preclude inclusion in our registry of
Knowledge
> Classification Systems that have not yet been related to
others
> by such
> logical specification. Such KCSs will serve as a knowledge
> resource
> for extension of the COSMO, and if they can be related to
other
> KCSs in
> any way, may also help to improve both the breadth and
accuracy
> of the
> COSMO, but also searching capabilities for search tools that
use
> these
> classifications.
>
> Pat
>
>
> Patrick Cassidy
> MITRE Corporation
> 260 Industrial Way
> Eatontown, NJ 07724
> Mail Stop: MNJE
> Phone: 732-578-6340
> Cell: 908-565-4053
> Fax: 732-578-6012
> Email: pcassidy@xxxxxxxxx
>
>
> -----Original Message-----
> From: ontac-forum-bounces@xxxxxxxxxxxxxx
> [mailto:ontac-forum-bounces@xxxxxxxxxxxxxx] On Behalf Of
John F.
> Sowa
> Sent: Tuesday, November 01, 2005 10:02 AM
> To: ONTAC-WG General Discussion
> Subject: Re: [ontac-forum] Surveyed Ontology "Library"
Systems -
> - parts
>
> Nicolas, Pat, Barry, et al.,
>
> This thread is getting into issues that are covered
> by the proposal for a lattice of theories:
>
> 1. All theories that anybody might propose about
> any subject whatever would be registered in a
> standard form in a metadata registry. Registering
> something does *not* imply any official status
> other than a commitment to save it in a convenient
> place for other people to examine it, use it, and
> comment on it.
>
> 2. Some theories in the registry would be more general
> and more widely reusable than others. Those are the
> ones that would eventually become the core of many,
> if not most practical ontologies. But there would be
> no need for an a priori blessing or canonization of
> any particular theory. Instead, the users would
> "vote by their feet", so to speak, in deciding for
> themselves which ones to choose for any particular
> application. The various choices and patterns of
> use and reuse would be added to the commentary in
> the registry.
>
> 3. In order to keep track of how theories are related
> to one another it is essential to show how they
> can be derived from or be converted into one another
> by the AGM operators for belief revision: contraction,
> expansion, and revision.
>
> 4. The three AGM operators define a lattice, in which
> the partial ordering defined by specialization and its
> inverse, generalization: expansion adds axioms to a
> theory to make it more specialized; contraction deletes
> axioms from a theory to make it more generalized; and
> revision does contraction followed by expansion in
> order to move from one theory to another, which is a
> sibling of a common parent.
>
> To use the example of part-whole relations, there are large
> numbers of axioms for many different variations. See, for
> example, the excellent book by Peter Simons called _Parts_,
> which goes into great detail about many different
> axiomatizations
> and their relationships to one another. Peter did not
organize
> the theories in a lattice, but it would be possible to do
so.
>
> In summary, we could adopt the current work on metadata
> registries as a means of registering theories and making
them
> available for further use, reuse, commentary, and analysis.
> One important aspect of the analysis would be to demonstrate
> how the various theories are related by the three AGM
> operators (to which I suggest a fourth operator called
> "analogy", which renames the predicates in a theory while
> preserving the implicational structure).
>
> The result of the analysis would be a step-by-step
> construction of a hierarchy of theories, ordered by
> specialization/generalization. An important aspect of
> the registry would be the ability to comment on the
> theories to show which ones are more widely used or
> more relevant to various kinds of applications.
>
> In short, analysis demonstrates the theoretical
relationships
> among the theories, and commentary demonstrates the
practical
> patterns of use and reuse for various applications. Both
> are necessary for a growing and evolving system.
>
> John Sowa
>
>
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