**Previous message:**Robin B. Lake: "Re: Request for guidance"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Robert Dodier: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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

*> Btw, I doubt that the fact that you know something is reflected by
*

*> probabilistic logic, without your formalizing it in any way.
*

That is =EXACTLY= what Bayesian probability theory is all about !!!

In Bayesian probability theory, _ALL_ probabilities are conditional

on the knowledge base one is willing to apply to the problem at hand.

The conditional probability P(A|{B}) in Bayesian theory is the degree

of confidence one has in the truth of Boolean proposition 'A', given

that the set of Boolean propositions {B} (the knowledge base one is

willing to apply to the problem) is assumed to be true. The Laws of

probability and Bayes theorem provide all the tools one needs to reason

about such `uncertain' Boolean propositions, as well as to incorporate

new data into one's knowledge base. See G. Larry Bretthorst's paper

``An Introduction To Model Selection Using Probability Theory As Logic''

<http://bayes.wustl.edu/glb/model.ps.gz>, or the draft of E. T. Jaynes'

magnum opus ``Probability Theory: The Logic of Science''

<http://bayes.wustl.edu/etj/prob.html>.

*>> 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.
*

*>...And that is what all Bayesian probabilities are conditioned on: The set
*

of Boolean popositions one is willing to take as axiomatic and relevant to

the problem at hand.

-- Gordon D. Pusch

perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'

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**Next message:**Ulrich Bodenhofer: "RE: How to quantify the quality of fuzzy expert system?"**Previous message:**Robin B. Lake: "Re: Request for guidance"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Robert Dodier: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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