Fuzzy Inference as Deduction

It is shown that much of fuzzy logic can be understood as classical deduction in a many-sorted many-valued Pavelka- Lukasiewicz style rational quantification logic.

Abstract

The term fuzzy logic has two different meanings -broad and narrow. In Zadeh's opinion ([19]), fuzzy logic (in the narrow sense) is an extension of manyvalued logic but having a different agenda- as generalized modus ponens, max-min inference, linguistic quantifiers etc. The question we address in this paper is whether there is something in Zadeh's specific agenda which cannot be grasped by >classical>, >traditional> mathematical (many-valued) logic. We show that much of fuzzy logic can be understood as classical deduction in a many-sorted many-valued PavelkaLukasiewicz style rational quantification logic. This means that, besides the linguistic or approximation aspects, the logical aspect (symbolic, deductive) is present too and can be made explicit.