Fuzzy Modal Propositional Logic And Generalized Tautologies

With the wide application of knowledge representation and knowledge inference in Fuzzy Modal Logic, more and more people put emphasis on the study of modal logic. First we study the theory of algebra of general in the wider sense. The concept of variable dimension operation, the concept of type in the wider sense and the algebra of general in the wider sense are defined. Then the concept of Fuzzy Modal Propositional Logic is put forward, the operation of Fuzzy Modal Propositional Logic is defined. We study the semantic of the Fuzzy Modal Propositional Logic. The fuzzized Kripke semantic, α -tautology and α -imply are defined. According to the difference condition of fuzzy relations R., reduction of the fuzzy modalities are discussed. The operation of ┐; ^;→;□;◇ in the evaluation lattice is defined. Then on the basis of the theory of algebra of general in the wider sense, we extend the system of Ln ,W and W . The system of MLn , MW andMW are defined. We extend professor Wang Guo-jun 's generalized tautological theory on Ln, Wand W|- to MLn, MW and MW|- , then discuss the properties and classification of the generalized tautology. On Ln, there is only one α -tautology. It is 1/2 -tautology. On ML2n, there is only one α -tautology. It is. n/(2n-1)--tautology. On MW and MW ,there are three generalized tautologies. They are 1/2 -tautology, (1/2)~y -tautology and tautology. At last, we study the properties of ∑-generalized tautology on MW .