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Re: [ontolog-forum] CL, CG, IKL and the relationship between symbols in

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 25 Dec 2007 02:35:41 -0500
Message-id: <4770B2CD.10505@xxxxxxxxxxx>
John B,    (01)

This thread has been ranging over too many complicated questions
at the same time.  It may be be better to clarify one narrow point
at a time and relate them later.    (02)

So let me put aside the following very important topics:
natural languages, psychology, percepts, perception, Semantic Web,
practical applications, and all philosophical issues about the
meaning of 'meaning'.    (03)

I don't want to forget them forever, but I just want to ignore
them for the moment in order to clarify one single issue:
a Tarski-style model-theoretic semantics.    (04)

What Tarski did is to define a formal method for evaluating
the truth values of sentences in terms of a model.  Following
are the basic ideas:    (05)

  1. Some formal language L, which would typically be some
     version of logic.  For the present, we can assume that L
     is some dialect of Common Logic, but the same ideas would
     apply to a much larger range of logics.    (06)

  2. The notion of a set D called the _domain_, which contains
     all the individual objects or entities that are being
     considered.  Sometimes D is called the _universe of discourse_.    (07)

  3. The notion of a model M, which consists of some domain D
     and a set R of relations, which relate objects in D.  For
     example, if r is a dyadic relation in R, then for any x and y
     in the domain D, r(x,y) has the truth value T or F.  In general,
     R may contain monadic, dyadic, triadic, or arbitrary n-adic
     relations (CL also allows 0-adic relations, which may be
     considered proposition constants.)    (08)

  4. The notion of an evaluation function Phi, which for any sentence
     s in L and any model M, determines a truth value T or F.  That is,    (09)

       For every sentence s in L and model M, Phi(s,M) = T or F.    (010)

If you want to read what Tarski himself said, I put a copy of his 1944
paper on the subject on my web site:    (011)

     The Semantic Conception of Truth    (012)

This is a more discursive tutorial on the subject than Tarski's
original paper from 1933.  Many people have complained that there is
more to meaning than what Tarski said, and he would have agreed.
His title was not "The Meaning of 'meaning'", but a more modest
claim "The Semantic Conception of Truth".    (013)

John Sowa    (014)

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