Path: utzoo!utgpu!water!watmath!clyde!att-cb!ihnp4!ucbvax!watdragon.waterloo.EDU!emneufeld
From: emneufeld@watdragon.waterloo.EDU (Eric Neufeld)
Newsgroups: comp.ai.digest
Subject: Re: FUZZY LOGIC VS. PROBABILITY THEORY
Message-ID: <5241@watdragon.waterloo.edu>
Date: 19 Feb 88 15:56:57 GMT
References: <8802180658.AA11175@ucbvax.Berkeley.EDU>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: Eric Neufeld <emneufeld%watdragon.waterloo.edu@RELAY.CS.NET>
Organization: U. of Waterloo, Ontario
Lines: 45
Approved: ailist@kl.sri.com


In article <8802180658.AA11175@ucbvax.Berkeley.EDU> golden@FRODO.STANFORD.EDU
(Richard Golden) writes:
>I am not an expert in Fuzzy Logic or Probability Theory but I have examined
>the literature regarding the foundations of Probability Theory and the 
>derivation of these foundations from basic principles of deductive logic.
>[...]
>The reference from which these arguments are based is given
>by Cox (1946). Probability Frequency and reasonable expectation.
>American Journal of Statistical Physics, 14, 1-13.
>[...]
>To my knowledge, the axioms of Fuzzy Logic can not be derived from
>consistency conditions generated from the deductive logic so I conclude
>that Fuzzy Logic is not appropriate for inferencing.  Any comments?!!!


The interest in reasoning with and about uncertainty in AI has sparked a
re-investigation into foundations of Prob. Theory.  Cox's theorem has become 
an important result for those interested in prob. theory as a measure of
belief.  You may be interested in the following references:

Proceedings of the AAAI Workshop on Uncertainty and AI: 1985, 1986, 1987.
A number of articles investigate the relationship between formal prob. theory 
and the various alternate formalisms: Fuzzy, Certainty Factors,
Dempster-Shafer.  Note articles by Cheeseman, Grosof, Heckerman and Horvitz.

Kyburg, Henry E- Bayesian and Non-Bayesian Evidential Updating, AI Journal,
Vol 31, 1987.  Investigates probabilistic assumptions underlying
Dempster-Shafer Theory.

Heckerman et al: AAAI-86: "A Framework for comparing alternate formalisms..."
Has been described as a presentation of Cox's result to the AI community.

Computational Intelligence: Upcoming issue (delayed in printing) Contains a
polemic article by Peter Cheeseman on probability theory (versus everything
in the world) and responses by various researchers, etc.

Aleliunas, Romas: "Mathematical Models of Reasoning".  Contains a
generalization of Cox's result to topologies other than real-valued
continuous [0,1] probability.  University of Waterloo Tech Report.

Eric Neufeld
Dept. Computer Science
University of Waterloo
Waterloo Canada