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From: hvirtanen@abo.fi (Harry Virtanen)
Newsgroups: comp.lang.prolog
Subject: Fuzzy Prolog
Message-ID: <6921.26ebb2bb@abo.fi>
Date: 10 Sep 90 15:35:23 GMT
Organization: Abo Akademi University, Finland
Lines: 43

I have recently been developing the theoretical foundations for a Fuzzy Prolog
system, called LukLog, a connection between Lukasiewicz logic and logic 
programming.

I know of two other Fuzzy Prolog systems, PROLOG/P (developed in sweden) and
PROLOG-ELF (developed in Japan). These two systems are built around the "fuzzy"
connectors
		a'   = 1-a  	  (negation, NOT)
		a^b  = min(a,b)   (intersection, AND)
		avb  = max(a,b)   (union, OR)
		a<-b = max(1-b,a) (implication)
where a, b are truth values (uncertainty factors) in the unit interval.
Given the following Fuzzy Prolog program

	(A<-B1^B2^B3)<-0.9.   % 0.9 denotes the uncertainty of the implication
	(B1<-)<-0.9.
	(B2<-)<-0.7.
	(B3<-)<-0.8.

and the goal <-A gives the truthvalue of A as 0.7.

LukLog is however built on the following functions/connectors

		a'    = 1-a
		a^b   = max(a+b-1,0)
		avb   = max(a,b)
		a<-b  = min(1-b+a,1)

Given the above program and the same goal, gives the truth value of A as 0.3.

I'm planning to present a paper (if accepted) on this subject at the IFSA 91'
Brussels congress. Any comments, or information on other existing Fuzzy Prolog
systems are welcome (personal mail or in this newsgroup).

Harry Virtanen
Abo Akademi University
Department of Computer Science
DataCity
Turku, Finland
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