Computational Logic Seminar
SFU Canada Research Chair in Cognitive Science
Philosophy, Linguistics and Computing Science
Date: Thursday Feb. 5, 2004 @ 1:30pm
Place: ASB 9705
Theorem Proving in Fuzzy Logic (joint work with Chris Lepock, Guang Li, and Dirk Henkemans)
The purpose of this talk is to introduce propositional Fuzzy Logic and some of its peculiarities, to present a method of showing the validity of a certain group of arguments in fuzzy logic, and to give a demonstration of an implemented system that does this. Fuzzy Logic replaces the two truth values 0 and 1 with the real values in the interval [0..1]. And it gives new interpretations of the traditional propositional connectives; and as well, some fuzzy logicians have advocated new connectives. It can be seen that there are a non-denumerable number of different functions that are definable on the [0..1] real interval, and since there are a finite number that can be employed in any representation, propositional fuzzy logic is expressively incomplete. Fuzzy logic also has the feature that it is not semantically compact, and so there are valid arguments with an infinite number of premises for which there is no valid argument with only a finite number of these premises. This means that there cannot be a general theory of argumentation that is complete.
Nonetheless, there might be some interest in that subportion of fuzzy logic of arguments with a finite number of premises. This is not (necessarily) the same as determining whether a particular formula is or is not semantically valid, since in the usual formulations of fuzzy logic, there is no connective that obeys the deduction theorem: that is, there is no connective * such that A,B,…M,N |- Z iff A,B,…M |- (N*Z). So, the various methods of determining tautologousness of a formula of fuzzy logic do not necessarily carry over to arguments. I will introduce tableaux systems generally, and show how they work in finitely-many-valued systems, and then show what modifications are needed for the infinite-valued case. Then I will show an implementation that does this.
BRING YOUR FAVOURITE FUZZY LOGIC FORMULAS/ARGUMENTS FOR ME TO TEST OUT! (I am looking for more and more nice examples).