From: Osher Doctorow [log in to unmask], Wed. Jan. 30, 2002 11:39AM
I specialize in the mathematics of fuzzy multivalued logics,
probability-statistics, as well as mathematical modeling and mathematical
physics. AI and Machines typically use Bayesian methods in
probability-statistics, which correspond to Product/Goguen fuzzy multivalued
logic and to division of probabilities,
while subtraction of probabilities corresponds to Lukaciewicz propositional
or Rational Pavelka predicate fuzzy multivalued logic. It is sometimes
mistakenly thought that division and subtraction are interchangeable by
taking logarithms of quotients and then re-labeling the new subtraction
logarithmic variables, but in fact it can be proven that there is no 1-1
functional relationship between y/x and y - x for real x, y or even x, y
confined to the interval [0, 1], and even functional relationships in one
direction do not in general hold. In addition, counterexamples in
probability-statistics can easily be found since log X and X generally have
different probability distributions for random variables X.
I have just applied Lukaciewicz and Rational Pavelka fuzzy multivalued
logics and their probability-statistical analog Logic-Based Probability
(LBP - which my wife Marleen and I introduced in 1980) at
http://www.superstringtheory.com/forum (section Cosmology VII) in a series
of several postings entitled Super-Laser Conjecture on
Black-White-Wormholes. Although this is physics/astrophysics, many of my
other applications are in or related to AI and Support-Vector-Machines..
For fairly detailed abstracts of 72 of my papers (and several co-authored
papers with my wife Marleen),
see http://www.logic.univie.ac.at, Institute for Logic of the University of
Vienna (after accessing the site, select in this exact order: 1. ABSTRACT
SERVER, then 2. BY AUTHOR, then 3. my name).
Osher Doctorow Ph.D.
Formerly (and still intermittently in parts) California State Universities
and Community Colleges
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