Semantics of Propositional Fuzzy Modal Logic with Evaluated Syntax and its Application to Fuzzy Decision Implications

Abstract

This paper deals with propositional fuzzy modal logic with evaluated syntax based on MV-algebras. We focus on its semantical theory from the viewpoint of Pavelka's graded semantics of propositional fuzzy logic, investigate the L-tautologies based on different Kripke frames. We also define the notion of L-semantical consequence operation, its some basic properties are obtained. Finally, this paper considers the fuzzy decision implications in propositional fuzzy modal logic with evaluated syntax based on MV-algebras, and presents a kind of semantical characteristics of fuzzy decision implications. Moreover, we introduce the notions of possible and necessary fuzzy decision implication, and their semantical characteristics are presented as well.

Keywords

• Propositional fuzzy modal logic
• Evaluated syntax
• L-tautology
• MV-algebra
• Consequence operation
• Fuzzy decision implication