Re: Models and Depictions

schubert@cs.rochester.edu
Date: Tue, 11 May 93 18:19:54 -0400
From: schubert@cs.rochester.edu
Message-id: <9305112219.AA15008@ash.cs.rochester.edu>
To: cg@cs.umn.edu, interlingua@ISI.EDU, schubert@cs.rochester.edu,
        sowa@turing.pacss.binghamton.edu
Subject: Re:  Models and Depictions

John,

To wind things down, maybe we should endeavor to keep each response to
half the length of its predecessor, till we're down to "ha!" "no!", etc.
Actually, I'll strive for zero length after the following.

You say (correctly I'm sure) Tarski restricted himself to formalized
languages. This does not entail that the domain of discourse must
consist of formal symbolic or mathematical objects (as you seem to
believe).

There ARE functions from symbols to real-world objects. Here's one,
called 'F': F has 2 elements; the first element is an ordered pair
consisting of the letter 'H' and the person, Pat Hayes; the second
element element is an ordered pair consisting of the letter 'S' and 
the person, John Sowa. I could do all sorts of uncontroversial math
with this function -- forming Cartesian products, inverses, etc. (and
so could you, I'm sure), with no harm to anyone. I'm assuming there's
only one of you, which your prodigous email output may cast doubt on.
Whether or not you and Pat have sharply defined boundaries and whether 
it's possible to design a formalized Pat Hayes- recognition procedure,
or John Sowa recognition procedure, are intriguing questions ;->, but 
beside the point.

When I say specialized representations are "in principle" dispensable,
I am saying that they are dispensable at some computational cost.
Long ago, the KR systems whose designs I worked on used no special
representations of times, colors, sets, etc; they worked all the same.
The "newer" ones (1982-93) use specialists, and work better.

John, you surely don't want to say that the formalized apple- and 
planet-recognition procedures I rhetorically asked about (and by 
extension, procedures for all other objects Newton regarded as subject 
to his laws) can be found in the works of Ptolemy, Galileo, and Bacon?! 
If so, we're off into a discussion about formality ... no, let's spare 
everyone.

You say that model theory is "a method of computing denotations". It's
not, and that's the crux of our disagreement. 

Anyway, you say that I've summarized your position fairly accurately
in my last note to "interlingua", and that is probably as close as we
can get to agreement.

Len