Newsgroups: comp.ai.fuzzy
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From: madhv-s@acsu.buffalo.edu (Sri_G)
Subject: Re: Fuzzy theory or probability theory? 
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Date: Sat, 3 Dec 1994 23:46:06 GMT
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S. F. Thomas (sthomas@decan.gate.net) wrote:

: I still insist that any utterance "A and not A" has no meaning in 
: natural language, at least not in the normal sense of the conjunctive
: "and".  

I agree. The *utterance* "tall and not tall" is simply incoherent.
Interestingly, it is considered coherent to say "I was both happy and
unhappy [at the same time]". This may be considered eliptical for "I
was partly happy and partly unhappy". Supposing I have a ball that is
blue in some portions and green in others, the ball is partly blue and
partly non-blue, and it we stretch things a bit, it may be coherently
said of the ball that it is "blue and non-blue".

The conjunctive "and" here is being used *not* to join contradictory
propositions about the ball, but to join propositions about different
parts of the ball. This, however, is *not* the sense of the conjunctive
"and" in "tall and not tall".

: 
: Now, I do not disagree that your basketball player's
: height could be at one and the same time both tall to some degree, and 
: not tall, to some degree.  But this is at a higher level of language
: which recognizes variation with respect to speaker, and variation with
: respect to time, for a given speaker. 

I wonder how the dependence of the membership function on the speaker
is handled in practice. Is there an alternative to having different
membership functions tall1, tall2 ...., one for each speaker ?  (In
that case, if speaker 1 says "the man was tall", and speaker 2 says
"the man was not tall", this could be represented as "tall1(x) and not
tall2(x)", which would not violate NC).

: The other "out" has of course to do with the passage of time.  A
: competent speaker of the language could of course at one time say
: "the perpetrator is tall", and at another time say "the perpetrator is
: not tall".  Nobody is perfectly consistent in his use of language.  A
: jury would, I think, be understanding of such little inconsistencies
: if the statements were taken at different times.

Errr... if these two statements were to be made by the same witness on 
the stand within the course of a trial, even a dim-witted lawyer would
pounce upon it as an inconsistency in the witness's testimony ...

: Quite so.  In the redevelopment of fuzzy set theory found in
: "Fuzziness and Probability", I do not argue in general with the min-max
: rules.  But I do assert that they do not always apply.  And the theory
: says precisely when which rule should apply, among (i) the min-max
: rules (ii) the product and product-sum rules and (iii) the bounded-sum
: rules.  Basically, one needs a notion of semantic consistency between
: terms.  When terms are "consonant" under this notion of semantic 
: consistency, then the min-max rules apply.  This applies, for example,
: to the terms "tall" and "very tall".  When terms are "dissonant"
: under this same notion, as for any term and its negation, the bounded-sum 
: rules apply, which do not violate the law of (non-)contradiction.  The product
: and product-sum rules apply for terms which are semantically independent,
: eg. when different speakers are involved, or the same speaker at 
: different times, or different universes of discourse.

Couldn't agree more.

- Sri_G

-- 
Sriganesh Madhvanath
Grad student, Dept of CS, SUNY at Buffalo      email: madhv-s@cs.buffalo.edu
