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Re: [uos-convene] UOS Tues Mar 14 topics? A short proposal

To: Upper Ontology Summit convention <uos-convene@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 12 Mar 2006 20:57:04 -0800
Message-id: <4414FBA0.8050202@xxxxxxxxxxx>
Chris and Leo,    (01)

I agree with Chris that subsumption is only one of the
important relations among any collection of theories.
In fact, I do talk about other relations, including
relative interpretability.    (02)

CM> The idea — induced simply by the fact that, for any two
 > theories, one is a subset of the other or not (in which case
 > the theories are not on a common branch of the lattice) — is
 > meant only as a helpful image (I think John himself agrees),
 > not as anything implementable (not that Leo is suggesting
 > otherwise).    (03)

Actually, the partial ordering is not subset, but implication
or entailment (which are equivalent for FOL theories).  Most
subsets and supersets of a theory are not theories, and the
union of two theories is usually not a theory.    (04)

Furthermore, the possible paths through the lattice happen to be
*identical* to the AGM operators for belief revision, which has
a very large and fruitful literature.  In fact, *every* method
proposed for nonmonotonic logic has been shown to be equivalent
to a method of belief revision:  in effect, all known methods of
nonmonotonic reasoning correspond to a walk through the lattice
of theories.    (05)

CM> The really important subsumption relation between ontologies
 > is relative interpretability, i.e., whether one ontology O1 can
 > be mapped into another O2 in such a way that the content of O1
 > is preserved in perhaps a conservative extension of) O2, albeit
 > in the terminology of O2.    (06)

I agree that relative interpretability is important.  But who
uses the word "subsumption" for it?  The word I use is "analogy",
which I define as a renaming of one or more entities (usually
predicates) of a theory.  Analogy creates "jumps" across widely
separated parts of the lattice induced by the AGM operators.
I certainly agree that it is an important addition.    (07)

CM> So it strikes me that it might be best to play down the lattice
 > of theories, both because it is arguably too coarse and also
 > because too many folks seize upon the image and think it buys
 > something practical.    (08)

Obviously, it doesn't buy anything practical since the infinite
lattice is never going to be implemented by anyone.  However, I
have found it a convenient pedagogical tool for talking about and
classifying the operations of combining, extending, and revising
theories.    (09)

John    (010)

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