# Re: Thomas' Fuzziness and Probability

From: Stephan Lehmke (Stephan.Lehmke@cs.uni-dortmund.de)
Date: Tue Aug 21 2001 - 06:57:43 MET DST

• Next message: Andrzej Pownuk: "Re: Thomas' Fuzziness and Probability"

In article <m28zgeg6zd.fsf@pusch.xnet.com>, Gordon D. Pusch writes:
> 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.

[...]

>>
>> 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.

I hate to burst your bubble, but that's exactly the same in _any_ form
of knowledge representation by logical formulae. Whether the
underlying logic is classical, fuzzy, probabilistic, possibilistic,
bayesian, dempster/shafer or any other of the myriad variants and/or
combinations might change the semantics of computed degrees associated
with derived formulae, but it doesn't change in the least the general
ability of the system to deal with background knowledge.

So the question how well background knowledge is handeled is
completely unsuitable for distinguishing between probabilistic and
fuzzy logic.

regards
Stephan

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