On Thu, Jun 01, 2006 at 09:29:43AM -0400, John Sowa wrote:
> Chris,
>
> I don't think this issue is worth a lengthy debate, since
> we aren't going to take any kind of action based on it. (01)
Ok, then stop replying. :-D (02)
> But I'll just clarify a few points. (03)
I thought I did that. :-) (04)
> That's comparing apples to grapefruit: (05)
And I thought that was one of my points...or are you responding to that
point? (06)
> > 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.
>
> First of all, PSL is a collection of axioms stated in some
> version of logic, such as KIF or CL. And OWL is a syntax
> for stating some subset of what is expressible in CL. (07)
OWL is *not* (merely) a syntax. Neither is PSL. Both PSL and OWL have
their OWN model theories. (Curiously, only informal versions of PSL's
model theory can be found on the PSL web site, but OWL's is here:
http://www.w3.org/TR/owl-semantics/rdfs.html) Granted, insofar as PSL
uses KIF, and OWL could use it, since KIF is CL (Common Logic)
conformant, the model theory of CL takes care of the semantics of the
basic logical constants used in PSL and OWL axioms. But both PSL and
OWL (especially OWL) have a sizable number primitives whose
interpretations are *fixed* in their respective model theories -- in
effect, they take on the status of logical constants. And that is where
you look if you want clearly to understand their intended meanings and
logical connections. (08)
> The creative work in defining the structures of PSL, or any such
> theory, was in the analysis of the informal concepts of time and
> process, (09)
Right, in defining those structures so as to expand upon and clarify the
informal concepts and write axioms to capture them. Couldn't agree
more. (010)
> translating mental models into diagrams on the blackboard (or
> whiteboard), thinking up good mathematical structures for representing
> those diagrams, writing axioms that characterize those structures, and
> testing their usefulness by applying them to a wide range of practical
> examples. That's where all the real "meaning" lies. (011)
Well, I'm not all that clear on just what a mental model is, but point
taken that inner representations and such have an important cognitive
role to play in the overall KR picture. As for diagrams, those are just
a type of representation language, usually a weak first-order language.
But I certainly agree that all of these are, or indicate, aspects of
"meaning" in the broader -- and for practitioners especially, more
relevant and "creative" -- sense. Surely you don't think I would
disagree with any of this (though I might express it differently :-) . (012)
> The mechanical process of turning the crank to pop out denotation "T"
> for each axiom is an important exercise to ensure that the loose ends
> have been tidied up. But that is the tiniest and least creative part
> of the job. (013)
Well sure, fine, outstanding, I'm down with that. :-) But again, you've
sort of shifted the issue to creativity and the broader notions of
meaning, which were never my concern in this discussion. I've only
tried to point out clearly where the role of model theory fits into the
larger picture. You seem stuck on the idea that I'm saying that it is
the largest and most important piece of the puzzle. I've never said
that. Other than that mischaracterization, I've found almost nothing to
disagree about in anything you've said. (014)
> > Well, blame is appropriate if their ignorance is culpable.
>
> Hao Wang is certainly not ignorant of logic, model theory,
> etc. (015)
You left out the smiley, which was an important part of the intended
semantics. :-) Be that as it may, even very smart people can say dumb
things -- as you often point out with regard to folks like Kripke,
Montague, and Wang's mentor, Quine. The remark was meant only as a
gentle rebuke toward those who would castigate model theory as a
"pathetic theory of meaning". Such a claim only demonstrates ignorance,
or willful disregard, of model theory's role in the overall discipline
of knowledge representation. If Wang ever said something to that
effect, he said something dumb (though I doubt very much he ever did). (016)
> I highly recommend his book, _Beyond Analytic Philosophy_. (017)
Well, thanks, that's kind of you, John, it is indeed a fine book and I
too recommend it to the one or two people other than the two of us who
might still be reading this exchange. :-) I won't offer any
counter-recommdendations, as I wouldn't want to give the impression that
you need to do a little rudimentary reading to clear up some elementary
confusions. (018)
> > But to castigate model theory on those grounds is to miss the
> > point badly.
>
> Neither I nor Wang ever castigated model theory. (019)
Of course not, and I have never claimed otherwise. The target of my
remarks, again, was those who find model theory a "pathetic theory of
meaning". Is that not to castigate model theory? Now, you did indicate
you felt some sympathy toward these folks, but, knowing you for as long
as I have, I suspect you were coming to their defense agains the likes
of Montague and others who have in fact overplayed the model theoretic
hand. (020)
> That would be like castigating the plus sign because it's trivial
> compared to a logarithm. The point I was making is that model theory
> is a necessary part of the formalism, but it's trivial compared to the
> amount of work that has to be done in analyzing the subject matter and
> writing the axioms. (021)
"Amount of work"? Is that supposed to be a rigorous measure of
importance? Once we have a syntactically and semantically well-defind
KR language, the theoretical work is done and the "amount of work" that
practitioners will do actually using it (if it's a good, or at least
popular, language) will dwarf the amount of work that went into its
design and construction. Similarly, the number of hours a typical 747
flies utterly dwarfs the amount of work that went into *its* design and
construction. Nonetheless, I'll bet even you will agree that the role
those Boeing engineers played was a pretty significant part of the
overall picture. ;-) (022)
-chris (023)
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