Responding to John Sowa: (01)
> 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. (02)
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? (03)
> 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. (04)
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. 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. (05)
BS (06)
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