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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 11:21:41 -0500
Message-id: <43679615.9040902@xxxxxxxxxxx>
Barry,    (01)

I am assuming that any policy of supporting interoperable
ontologies would presuppose a formal logic.  Without that,
there is no hope of success.    (02)

JS>> 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.    (03)

BS> Would this not impose significant constraints (in terms of
 > formalisms used) and costs (in terms of the hours of expert
 > manpower needed to translate existing ontologies into such
 > formalisms) in order to bring about a situation in which
 > the AGM operators can be applied?    (04)

I would assume that all ontologies would be specified in some
formally defined notation that could be translated to a common
form just by pushing a button.  The currently proposed ISO
standard for Common Logic, for example, already subsumes a
large number of common notations, including all the versions
used for the Semantic Web (e.g., RDF(S), OWL, and the more
recent proposals for rule-based languages).  CL also supports
a superset of the semantics of many other versions of logic,
including Z, Conceptual Graphs, and various semantically clean
Horn-clause languages.    (05)

This proposal allows people to use any language they prefer,
as long as it is automatically translatable to a common form.    (06)

BS> And we will get formal sophistication in regard to the latter
 > (e.g. in such a way that the AGM operators can be supplied)
 > only when the ontology community finally gets clearer about
 > the difference between instances and universals.    (07)

I completely agree.  And the best way to get people to understand
that point is to give them tools that enforce the distinction.
In logic, the distinction is very precise:  universals map
to things called types, predicates, relations, or functions,
and instances are referenced by variables that appear in the
arguments of those things.  (Of course, we also want to allow
quantifiers that range over functions, relations, and types,
but that is an issue to be discussed at the second step.)    (08)

BS> The problem is that Peter's book deals with part-relations
 > between instances (e.g. between this handle and this cup,
 > or between this footstep and this walk), where ontologies
 > deal with part (and other) relations between
 > types/classes/universals.    (09)

Yes, the definition of an ontology consists primarily in
definitions of universals.  But every application of an
ontology must apply those definitions to very concrete
instances.  An ontology of parts and wholes, for example,
is useless unless you can apply it to particular handles,
cups, and all the other instances of parts that are listed
in a database, knowledge base, web site, etc.    (010)

If you have a good logic notation, the distinction between
universals and instances is enforced by the tools, which
raise an error message when the constraints are violated.
That immediate feedback is essential for training people
to recognize the distinctions.    (011)

John Sowa    (012)

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