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