**Previous message:**Andrzej Pownuk: "Re: Thomas' Fuzziness and Probability"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Herman Rubin: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*> > 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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*>
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*> That is =EXACTLY= what Bayesian probability theory is all about !!!
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*> In Bayesian probability theory, _ALL_ probabilities are conditional
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*> on the knowledge base one is willing to apply to the problem at hand.
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*> The conditional probability P(A|{B}) in Bayesian theory is the degree
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*> of confidence one has in the truth of Boolean proposition 'A', given
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*> that the set of Boolean propositions {B} (the knowledge base one is
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*> willing to apply to the problem) is assumed to be true. The Laws of
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*> probability and Bayes theorem provide all the tools one needs to reason
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*> about such `uncertain' Boolean propositions, as well as to incorporate
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*> new data into one's knowledge base. See G. Larry Bretthorst's paper
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*> ``An Introduction To Model Selection Using Probability Theory As Logic''
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*> <http://bayes.wustl.edu/glb/model.ps.gz>, or the draft of E. T. Jaynes'
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*> magnum opus ``Probability Theory: The Logic of Science''
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*> <http://bayes.wustl.edu/etj/prob.html>.
*

Probability theory is related

with the question

"how often something happened".

When in each experiment we get the same results,

then this problem is not related with theory of probability.

We know the answers with probability one.

When I see that knowledge

of my students is related with probability,

(For the same question I got

different response.)

then I doubt about their knowledge.

Let us consider segment on the plane,

which is divided into two parts

T /_____ segment

T \

T

T Top part of the plane

T

XXXXXXXXXXXXXXXXXX

B

B

B Bottom part of the plane

B

B

Now we can ask the following question.

Is the segment at the bottom part of the plane?

The answers "NO" or "YES" are not perfect in this case.

We can build a non-probabilistic measure

which describe this problem.

m(segment | bottom)= Length(part B)/Length(part B + part T)

In this case

m( segments | bottom)=5/10=0.5

I think that this problem

is not related with probability.

(In each experiment we get the same result.)

Because of that in this case

we can't apply probabilistic logic.

I think that in real word

exist uncertain problems

which can't be described

by probability theory.

Andrzej Pownuk

---------------------------------------------

MSc. Andrzej Pownuk

Chair of Theoretical Mechanics

Silesian University of Technology

E-mail: pownuk@zeus.polsl.gliwice.pl

URL: http://zeus.polsl.gliwice.pl/~pownuk

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**Next message:**Herman Rubin: "Re: Thomas' Fuzziness and Probability"**Previous message:**Andrzej Pownuk: "Re: Thomas' Fuzziness and Probability"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Herman Rubin: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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