Responding to John Sowa (01)
> > One problem is that much of the best work in
> > biomedical ontology is not formulated in any
> > of the languages covered by CL.
>
>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. (02)
Unfortunately (in the case of the FMA, at least) only with a huge
amount of work. (03)
> > Another problem is that many of the ontologies
> > which are so covered are sealed off from each other
> > by the use of separate namespaces.
>
>That is always true of independent developments,
>but that is exactly the issue that any project
>designed to support interoperability must address.
>
>That is, in fact, one reason why I added the analogy
>operator to the AGM operators of expansion, contraction,he
>and revision. It enables theories that use different
>choices of names to be related to one another by specifying
>the name maps. (04)
Good. Who will specify them? Who will check them? Who will deal with
all those many cases where seemingly identical terms in different
namespaces have either no definitions or logically incompatible definitions? (05)
>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. (06)
Now they are more than disguised. The policy of enforcing namespaces
means that they are systematically separated. (07)
> 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)
This is a nice ideal, but attempts to establish CL-compatible logical
formalisms and name maps e.g. in domains like anatomy (where
considerably energy has been invested) have thus far been less than
impressively successful. (09)
>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. (010)
There is no dispute here. (011)
> > 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.
>
>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. (012)
Good.
BS (013)
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