**Previous message:**Ulrich Bodenhofer: "RE: How to quantify the quality of fuzzy expert system?"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Andrzej Pownuk: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

I (Robert Dodier) wrote:

*> > Consider a less-extreme example, then: let A = "the mayor is tall",
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*> > B = "the mayor is heavy", and B' = "the mayor is well-dressed". For the
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*> > sake of argument suppose that truth(B)=truth(B'). Despite the fact that
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*> > we know that there is some relation between height and weight, the
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*> > truth value assigned to a compound containing A and B is just the same
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*> > as what we get by putting B' in the place of B.
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Stephan.Lehmke@cs.uni-dortmund.de (Stephan Lehmke) wrote:

*> Again, i must ask whether the situation would change if two-valued
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*> logic were employed?
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I'm assuming that these propositions are not definitely true nor false,

so two-valued logic is not applicable here. Let's stick to the topic,

shall we?

*> [...] Fuzzy logic is about vagueness, not telepathy (whatever I
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*> know has to be reflected by the logical system, whether I care to
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*> write it down or not).
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*>
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*> Btw, I doubt that the fact that you know something is reflected by
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*> probabilistic logic, without your formalizing it in any way.
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True enough, but probabilistic logic has the advantage that the

list of probabilities needed to answer a particular question can

determined automatically. This, I believe, is extremely important

in constructing systems for automated inference.

For example, suppose I ask a Bayesian robot about p(A B). The robot

says I need to tell it either p(A) and p(B|A) or p(B) and p(A|B).

The relation between A and B doesn't need to be formalized to get this far.

The situation is more interesting in problems with many variables,

some of which have stated values, and the goal is to compute a

distribution over one or more variables. In this case, it is non-trivial

to determine which relationships come into play. However, the laws

of probability always allow one to determine which formal relations

are needed. Once these relations are stated, the computations can begin.

*> > There is a two-fold drawback of defining truth value of a compound
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*> > strictly as a function of truth values of its parts. (i) You cannot
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*> > exploit information about the relation between A and B; even if you
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*> > know what it is, there is simply no place to put it in the computation
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*> > of the truth value of a compound proposition. (ii) The rules for computing
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*> > truth value of the compound don't tell you when you need to supply
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*> > some information about the relation between the parts.
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*>
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*> I think we're talking cross purposes here. Logic is not about
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*> computing truth values, but about drawing conclusions from assertions.
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Well, is it not the case that drawing conclusions, in fuzzy logic,

is accomplished by computing truth values?

*> Of course, it is perfectly possible to state the relations between A
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*> and B it the form of axioms, as I have pointed out before.
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No, this won't help. According to the usual rules of inference in

fuzzy logic, the truth value of a compound is a function of the truth

values of the parts alone, and therefore there is no place to enter

information about relations between the parts.

You can state all the axioms you want; there is no way to enter these

into the usual truth-functional rules. Perhaps you have in mind some

alternate rules -- if so, how do you know your rules take precedence?

More to the point, how would an automated system know which rules

take precedence?

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

**Next message:**Paul E. Keller: "Applications and Science of Computational Intelligence V"**Previous message:**Ulrich Bodenhofer: "RE: How to quantify the quality of fuzzy expert system?"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Andrzej Pownuk: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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