# Re: Thomas' Fuzziness and Probability

From: Gordon D. Pusch (gdpusch@NO.xnet.SPAM.com)
Date: Tue Aug 21 2001 - 12:33:46 MET DST

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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

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