On Wed, May 31, 2006 at 10:57:59PM -0400, John Sowa wrote:
> Right. If you are able to find a model, the most you have
> demonstrated is consistency. (01)
Well, yeah, in and of itself, that's what the existence of a model gives
you. But I'm wary of the implication here (?) that that is all that
model theory is good for. A good model theory for a language,
especially a somewhat complex one like PSL or OWL (or one capable of
some cute tricks like Common Logic), provides a very clear picture of
the *structure* of the information described by the language. In PSL,
for example, there are timepoints, objects, activity types, and activity
occurrences. The model theory shows very trenchently how these four
categories of thing fit together, especially with regard to activity
types and activity tokens. Granted, lots of ordinary users and workaday
ontologies won't much care about that if they've got a good process
modeling tool, for example, but the underlying model theory is what
makes such a tool possible, much like the underlying mathematics and
engineering that makes a good calculator possible. (02)
> I like this logic stuff, and I think it's valuable. But I really
> can't blame people who say that model theory is rather pathetic as a
> meaningful theory of meaning. (03)
Well, blame is appropriate if their ignorance is culpable. :-) Granted,
model theory is a mathematical theory of meaning for *formal* languages.
But insofar as formal languages are idealizations of certain aspects of
natural language, a good model theory can yield many deep insights into
the nature of meaning even in natural language, especially the way that
the meanings of complex epxressions depend upon the meanings of their
component parts. It is also very illuminating vis-a-vis the meanings
of, and semantic connections between, the logical constants
(quantifiers, intensional operators, etc). But OF COURSE model theory
isn't going to tell you much of anything about the "real world" meanings
of the nonlogical expressions like "chair" or "person", let alone
subtler senses of meaning deriving from perception and emotion. But to
castigate model theory on those grounds is to miss the point badly. (04)
Chris Menzel (05)
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