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Re: [ontac-forum] Surveyed Ontology "Library" Systems -- parts

To: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 01 Nov 2005 10:01:40 -0500
Message-id: <43678354.8080802@xxxxxxxxxxx>
Nicolas, Pat, Barry, et al.,    (01)

This thread is getting into issues that are covered
by the proposal for a lattice of theories:    (02)

  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.    (03)

  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.    (04)

  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.    (05)

  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.    (06)

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.    (07)

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).    (08)

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.    (09)

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.    (010)

John Sowa    (011)

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