Re: Thomas' Fuzziness and Probability

From: Stephan Lehmke (Stephan.Lehmke@cs.uni-dortmund.de)
Date: Mon Aug 20 2001 - 13:26:31 MET DST

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    In article <23af61c2.0108180659.1cbf8b83@posting.google.com>, Robert Dodier writes:
    > Stephan.Lehmke@cs.uni-dortmund.de (Stephan Lehmke) wrote:
    >
    >> Robert Dodier writes:
    >> >
    >> > Any such definition must ignore the relation between elements in a
    >> > compound: if truth(B')=truth(B), then in any proposition containing
    >> > A and B, I can swap in B' in place of B, and get exactly the same
    >> > truth value for the compound; whether the elements are redundant,
    >> > contradictory, or completely unrelated doesn't enter the calculation.
    >>
    >> It's exactly the same in two-valued logic. As fuzzy logic agrees with
    >> classical logic on the extremal truth values, there is no way the
    >> behaviour you observe can be avoided.
    >
    > Consider a less-extreme example, then: let A = "the mayor is tall",
    > B = "the mayor is heavy", and B' = "the mayor is well-dressed". For the
    > sake of argument suppose that truth(B)=truth(B'). Despite the fact that
    > we know that there is some relation between height and weight, the
    > truth value assigned to a compound containing A and B is just the same
    > as what we get by putting B' in the place of B.

    Again, i must ask whether the situation would change if two-valued
    logic were employed? Otherwise, obviously it has to be the same in
    fuzzy logic. Fuzzy logic is about vagueness, not telepathy (whatever I
    know has to be reflected by the logical system, whether I care to
    write it down or not).

    Btw, I doubt that the fact that you know something is reflected by
    probabilistic logic, without your formalizing it in any way.

    > There is a two-fold drawback of defining truth value of a compound
    > strictly as a function of truth values of its parts. (i) You cannot
    > exploit information about the relation between A and B; even if you
    > know what it is, there is simply no place to put it in the computation
    > of the truth value of a compound proposition. (ii) The rules for computing
    > truth value of the compound don't tell you when you need to supply
    > some information about the relation between the parts.

    I think we're talking cross purposes here. Logic is not about
    computing truth values, but about drawing conclusions from assertions.

    Of course, it is perfectly possible to state the relations between A
    and B it the form of axioms, as I have pointed out before.

    > To draw a
    > conclusion about a compound proposition, maybe you need to know something
    > about the relation between the parts and maybe you don't, but there's
    > no way to tell from the rules which is the case.

    This statement is unintelligible to me. Could you elaborate?

    regards
    Stephan

    -- 
      Stephan Lehmke     		 Stephan.Lehmke@cs.uni-dortmund.de
      Fachbereich Informatik, LS I	 Tel. +49 231 755 6434 
      Universitaet Dortmund		 FAX 		  6555
      D-44221 Dortmund, Germany             
    

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