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Re: [ontolog-forum] Next steps in using ontologies as standards

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 22 Jan 2009 09:58:32 -0500
Message-id: <49788998.4010902@xxxxxxxxxxx>
Pat C, Pat H, Azamat, Ali,    (01)

I'll start with the following exchange, which illustrates the
basic issues:    (02)

PC> I have said that a very large number of complex concepts (such
 > as, but not restricted to, concepts defined by necessary and
 > sufficient conditions) or theories can be represented as
 > combinations of the primitive concepts.    (03)

PH> It seems to me both more honest and more useful to say that we
 > have a number of alternative ontologies here, all describing the
 > same small group of basic ideas or concepts, but describing them
 > differently. Then there are indeed a small number of 'primitive'
 > concepts, but multiple ontologies of them, rather then one ontology
 > with many alternative 'primitive' concepts, all very similar but
 > subtly different, and all bearing the same rather diffuse
 > relationship to the normal English words or intuitive ideas.    (04)

I agree with Pat Hayes on this point.    (05)

Alan Cruse coined the term 'microsense' for the variations of
meaning of words in ordinary language from one context to another.
That same term applies to the formal notions of science, whose
microsenses vary from one theory to another.    (06)

JFS>> ... For example, the axiom F=ma relates force, mass, and
 >> acceleration without requiring any prior definition of any of
 >> those three terms.    (07)

AA> ... your interpretation of the fundamental law of mechanics
 > seems not so convincing. The laws of classical mechanics hardly
 > ever could be formulated without its fundamental concepts, such
 > as matter, energy, physical body, quantity, unit, dimension,
 > force, motion, extended from the top foundation classes as
 > substance, state, change, relationship, cause, duration, space.    (08)

I think we can all agree that people have intuitive ideas,
expressed in the words of ordinary language.  But the concepts
you cite have changed immensely over time.  A person who never
studied science thinks about them in ways that are closer to
Aristotle than Newton, and the changes that occurred during
the 20th century related those ideas in ways that were
previously unimaginable -- e.g., the idea that something could
be a wave and a particle at the same time or that matter and
energy are interchangeable.    (09)

Scientists refine those ideas through many years of painstaking
analysis and relate the measurable quantities in formulas.  But
there are no primitive "building blocks" that retain their shape
over time.  They do use analogies (e.g., the analogy between
water waves and electron waves) but those analogies are false
in many more ways than they are true.  Even when they use the
same words ('mass', 'energy', 'force', 'momentum'), the equations
they use to relate them are inconsistent with the old equations.    (010)

All scientific theories and formal ontologies are like that.
Scientists start with vague ideas and analogies to familiar
concepts, but they refine them and relate them in formulas
that are inconsistent with the old formulas.  There are no
such things as fixed "primitives".    (011)

AH> My understanding of Pat's points is that these primitives
 > are derived from theories that have axioms.    (012)

He repeatedly points to the Longman's dictionary, which was
designed for people learning English as a second language.
That dictionary uses a selection of about 2000 words as the
basic defining vocabulary, and Pat C claims that some number
of concepts -- either exactly or approximately corresponding
to that vocabulary would be suitable "primitives" for building
formal theories.  But he has never shown us how to construct
a single theory from some subset of such primitives.    (013)

AH> Would people agree that there is a large body of FOL theories
 > that are reused and common to many others? (Not necessarily in
 > the upper ontology sense of concepts being reused, but rather
 > that there are model theoretic structures being reused).    (014)

If by "reuse", you mean something like the operations on the
a lattice (or hierarchy) of theories, I certainly say yes.    (015)

The basic operators used to construct theories from theories
are generalization (deleting axioms), specialization (adding
axioms), analogy (relabeling the names in a theory to adapt
it to a different domain), and conjunction (forming a common
specialization of two or more consistent theories).  Many
large ontologies (Cyc and SUMO are examples) were constructed
by these operators.    (016)

AH> Is it not a worthwhile endeavor to collect and collate
 > these theories?    (017)

Certainly.  That is the main purpose of a registry/repository
for ontologies.  And I have recommended that the registry
also organize the theories in a hierarchy that emphasizes the
operations that relate theories to theories (generalization,
specialization, common generalization, common specialization,
and analogy).    (018)

AH> If you don't think this approach is feasible / reasonable,
 > do you have any alternatives to offer?    (019)

This approach has proved its usefulness in developing large
ontologies such as Cyc, SUMO, and others (even though they
haven't explained the methodology in exactly these words).
I wouldn't rule out other methods, but this approach is
a good place to start.    (020)

And by the way, I wouldn't even rule out Pat C's idea of
primitives, but the burden on him is to give us a single
example of a few primitives and a methodology for using them
to construct a theory.  Until we have at least one example,
there is nothing to consider.    (021)

John Sowa    (022)

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