**Previous message:**S. F. Thomas: "Re: Thomas' Fuzziness and Probability"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Stephan Lehmke: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Stephan.Lehmke@cs.uni-dortmund.de (Stephan Lehmke) wrote:

*> Robert Dodier writes:
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*> >
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*> > Any such definition must ignore the relation between elements in a
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*> > compound: if truth(B')=truth(B), then in any proposition containing
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*> > A and B, I can swap in B' in place of B, and get exactly the same
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*> > truth value for the compound; whether the elements are redundant,
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*> > contradictory, or completely unrelated doesn't enter the calculation.
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*>
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*> It's exactly the same in two-valued logic. As fuzzy logic agrees with
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*> classical logic on the extremal truth values, there is no way the
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*> behaviour you observe can be avoided.
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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.

*> If _you_ have some additional knowledge about how eye colors usually
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*> behave, you have to introduce this knowledge as an additional axiom,
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*> exactly as you would do in two-valued logic.
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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. 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.

Regards,

Robert Dodier

-- ``Socrates used to meditate all day in the snow, but Descartes' mind worked only when he was warm.'' -- Bertrand Russell############################################################################ This message was posted through the fuzzy mailing list. (1) To subscribe to this mailing list, send a message body of "SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at (2) To unsubscribe from this mailing list, send a message body of "UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com" to listproc@dbai.tuwien.ac.at (3) To reach the human who maintains the list, send mail to fuzzy-owner@dbai.tuwien.ac.at (4) WWW access and other information on Fuzzy Sets and Logic see http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info (5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html

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