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Topic: William A. Dembski: Random Predicate Logic I: A Probabilistic Approach to Vagueness
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posted 24. July 2002 21:44
Random Predicate Logic I: A Probabilistic Approach to Vagueness
by William A. Dembski
William_Dembski@baylor.edu
ABSTRACT—This is an old paper, written twelve years ago, that's been in cold storage ever since. I had always intended to get back to it and apply the formalism it develops, but other projects kept getting in the way. I finally decided to clean it up and get it into circulation, not only because it provides a more powerful and ultimately, I believe, more fruitful formalism than fuzzy logic, but also because I am eager to apply it to confirmation theory, logical paradoxes, and, most importantly from my view, to design-theoretic concepts. I want in particular to treat predicates that attribute complexity, specified complexity, and design as random predicates and see what fruit this reformulation will bear. Since Bart Kosko has shown that fuzzy logic cannot be subsumed under Bayesian techniques, and since fuzzy logic is strictly subsumable under random predicate logic, I intend, as it were, to transcend Bayesian techniques by moving to a completely different formalism. All of this, of course, constitutes a promissory note and will have to await "Random Predicate Logic II: Applications and Interpretations." The paper here merely lays out the basic formalism.
To read the entire paper, please click here
[ 24 July 2002, 21:49: Message edited by: Moderator ]
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gedanken
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posted 29. September 2003 01:13
Is it acceptable to resurect such an old thread? (Over a year ago). I ran across this in a search--serendipitously.
But a recent thread actually discussed issues of relevance.
Now I would note that Kosko has multiple books explaining why "Fuzzy Logic" cannot be subsumed into probability. (In fact he has once claimed that probability theory axioms can be derived from "first principles" from Fuzzy Logic axioms and/or concepts.
At this point I agree with Kosko's assertion from my own knowledge, but having no understanding of the formalism proposed in this paper or exactly what is meant. (This may be a different meaning of "probability" than I understand, for example. I have only lightly skimmed the paper.)
I do find that "Fuzzy Logic" is an approximation methodology--reducable to approximation theories in some sense. What my research has shown is that there is no single consistent means for combining the fuzzy membership functions that does not break down in the combinatorial explosion of complexity of relationships. Any fuzzy (or crisp for that matter) logic combination operaton set can only approximate refined description of relationships in the real world with some degree of a "music of the spheres" ad-hoc approximation.
Now that is probably the very point intended in Fuzzy Logic theory, that one can arbitrarily approximate what is needed, and do so with less symbology than with crisp logic.
In any case, here I have brought the thread forward for discussion. I shall not return to this until I have made substantial progress in another thread, but will do so at some point.
[ 29. September 2003, 02:32: Message edited by: gedanken ]
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