Graded Propositional Fuzzy Logic for Approximate Reasoning

摘要

For the task of approximative reasoning, in this paper, the graded semantics and syntax is developed for Lukasiewicz infinite-valued propositional logic on [0,1]. The relations among α -tautologies in the frame of graded theory are obtained. In a natural way, the fuzzy information based on a crisp set of formulas is defined. On this basis, some propositions analogous to those in the classical logic are proved, and the corresponding graded syntax is established. Moreover, we also establish the generalized deduction theorem by extending the classical deduction theorem.