Re: SUO: Lattice of Theories vs a Single Ontology
>Adam,
>
>I think you should be able to do just as you suggest, put things in
>different files. However, the real value of such an arrangement is on
>the representation level. You are creating modular theories. You now can
>deal with local consistency and local completeness, i.e., theory X is
>consistent, theory Y is consistent, but taken together they are
>inconsistent: why? Maybe because you can focus on a subset: X has A,B;
>Y has A, -B. Therefore they are consistent on A. Hence, create a theory
>Z which has A (or have your "intelligent" system which knows about the
>logical properties of theories/ontologies do so for you). Z can be
>viewed as the intersection of X and Y or as the meet of X and Y if they
>inhere in a lattice. The point is that X, Y, Z, are partially ordered
>theories or something stronger, part of a lattice.
>
>In fact, contrary to your guess, I think there are many highly separable
>components: a theory of mereotopology and variants (other theories with
>more or less axioms), a theory of
>collectivity-distributivity-cumulativity (for plurals, masses,
>organizations, etc., which will probably build on the mereotopology
>theories), theories of time (scalar, branching, point, interval),
>theories of events (processes, actions, states), theories of space,
>location, emotion, agency, planning, language, etc. And, as you go
>downwards, toward domain theories/ontologies, separability increases. A
>theory about military command and control is very distinct from a theory
>of business-to-business e-commerce, though of course they share
>theories.
Right. I would add that some theories actually have different uses in
different contexts, eg mereology and all the part/(w)hole theories
apply without internal change both to a 3-d case (where their
quantifiers range over pieces of 3-d space and surfaces are 2-d and
so on) and to a 4-d case (where their quantifiers range over
space-time extensions and surfaces have three dimensions, and so on).
Many mathematical theories of space generalize across dimensions, in
fact, which is a large part of the reason why they are so useful. But
if they are tied down to a single place in a larger theory, this
utility and generality is lost, because of course it would be
inconsistent to think of them in both ways *at the same time*.
Pat Hayes
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