Re: Contexts and quantifiers in KIF

sowa <sowa@turing.pacss.binghamton.edu>
Date: Fri, 16 Apr 93 03:08:54 EDT
From: sowa <sowa@turing.pacss.binghamton.edu>
Message-id: <9304160708.AA10706@turing.pacss.binghamton.edu>
To: cmenzel@kbssun1.tamu.edu, sowa@turing.pacss.binghamton.edu
Subject: Re: Contexts and quantifiers in KIF
Cc: cg@cs.umn.edu, interlingua@ISI.EDU, srkb@ISI.EDU

Chris,

I use the term "metaphor" in a very precise technical sense.
And I definitely do not use it in a pejorative sense.

In fact, I claim that metaphor is a fundamental mechanism of
language that enables a finite vocabulary to be extended to new
domains for which the terms were not originally intended.  It
is therefore an extremely powerful mechanism that can be of immense
value.  But it can also be the source of philosophical confusions
between the extended meanings and the original literal meanings
of a word.

If you have a chance, you might take a look at the book _Knowledge
Representation and Metaphor_ by Eileen Way, Kluwer, 1991.  Eileen
originally wrote that book as her PhD dissertation at SUNY Binghamton
under my supervision, and she also implemented a small conceptual
graph interpreter as part of the effort.  Her basic contribution is
the theory of "dynamic type hierarchies" in which metaphor is the
basic mechanism for introducing new concept types that refine and
extend the type hierarchy.

To apply Eileen's analysis to the Kripke-Montague sorts of "possible
worlds", I would say that you start with the concept type WORLD, which
originally applied to the everyday physical world we live in.  Then you
might observe certain patterns that occur in the real world that can be
mimicked by abstract patterns in set-theoretic constructions.  The next
step is to extract the following triangle from the type hierarchy,
which shows ENTITY as the least common supertype of both WORLD and
SET-THEORETIC-CONSTRUCTION:

                             ENTITY
                              /  \
                             /    \
                          WORLD  SET-THEORETIC-CONSTRUCTION

Then by lambda-abstraction, you construct a new concept type, which
is a subtype of ENTITY and a supertype of both WORLD and SET-THEORETIC-
CONSTRUCTION.  We might call that new type "GENERALIZED-WORLD":

   GENERALIZED-WORLD = (lambda x)(x is an entity that contains a pattern
       of individuals and relations that can serve as the extension of every
       true elementary sentence of a language L).

Then this new concept GENERALIZED-WORLD can be used as a basis for
a model theory where there is one subtype that has the real world as
an instance and another subtype that has an open-ended number of
set-theoretic constructions as instances.

This analysis is what I mean when I say that Kripke and Montague are
using the term "world" as a metaphor.  If they would explicitly admit
that they are using the word in a metaphorical sense, then I would be
happy to let them do so.  However, certain problems keep coming up
in that construction that make it difficult to work with a version
of model theory that mixes set-theoretic constructions and the real
world.  Therefore, I prefer to dispense with the metaphor and work
only with abstract constructions.  This gives me greater flexibility
in deciding which construction I choose to apply to the real world
for different purposes at different times.  That is important for
dealing with nonmonotonic reasoning, fuzzy logics, etc., where there
may be more than one model that is applicable and where there may be
a measure of goodness of approximation rather than an absolute truth
or falsity.

John