Barry, (01)
I'm not so sure about that: (02)
> One problem is that much of the best work in
> biomedical ontology is not formulated in any
> of the languages covered by CL. (03)
The fact that they haven't yet been defined in terms
of the CL semantics does not mean that they couldn't
be so defined. I strongly suspect that they could be. (04)
> Another problem is that many of the ontologies
> which are so covered are sealed off from each other
> by the use of separate namespaces. (05)
That is always true of independent developments,
but that is exactly the issue that any project
designed to support interoperability must address. (06)
That is, in fact, one reason why I added the analogy
operator to the AGM operators of expansion, contraction,
and revision. It enables theories that use different
choices of names to be related to one another by specifying
the name maps. (07)
It is rare that two independently developed theories are
identical except for names, but that is why you need to
specify the full lattice. Two theories on similar subjects
usually have many common generalizations that are disguised
by differences in naming. When you add analogy to the AGM
axioms, it enables the task of aligning ontologies to be
viewed as a walk through the lattice of theories, where
the paths are defined by the four operators: contraction,
expansion, revision, and analogy. (08)
That view gives you a theoretical framework for addressing
the problem. Then you can develop tools based on theorem
provers, analogy finders, etc., for aiding the task. A
fully automated approach will eventually be possible, but
the first step is to develop semi-automated tools that can
support the development, alignment, and reuse of ontologies. (09)
> But would also like to point out that some of the most
> interesting developments allow argument-variables to
> range over both instances and universals. Hence I think
> people need to understand the distinction independently
> of recognizing the need to use logical symbolism correctly. (010)
Yes, indeed. CL also supports quantifiers that range over
functions, relations, and types. In teaching people how to
use logic and ontology, I would start by teaching them the
rudiments with constant names for the universals. After
they feel comfortable with that, I would introduce the
option of quantifying over the universals as well. (011)
John (012)
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