Isn't Every Sufficiently Complex Logic Multi-Valued Already: Lindenbaum-Tarski Algebra and Fuzzy logic Are Both Particular Cases of the Same Idea

Authors

Andrzej Pownuk, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

5-2017

Comments

Technical Report: UTEP-CS-17-33a

To appear in Proceedings of the Joint 17th Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems, Otsu, Japan, June 27-30, 2017.

Abstract

Usually, fuzzy logic (and multi-valued logics in general) are viewed as drastically different from the usual 2-valued logic. In this paper, we show that while on the surface, there indeed seems to be a major difference, a more detailed analysis shows that even in the theories based on the 2-valued logic, there naturally appear constructions which are, in effect, multi-valued, constructions which are very close to fuzzy logic.