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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