Bilattices for deductions in multi-valued logic

Abstract In this exploratory paper we propose a framework for the deduction apparatus of multi-valued logics based on the idea that a deduction apparatus has to be a tool to manage information on truth values and not directly truth values of the formulas. This is obtained by embedding the algebraic structure V defined by the set of truth values into a bilattice B . The intended interpretation is that the elements of B are pieces of information on the elements of V . The resulting formalisms are particularized in the framework of fuzzy logic programming. Since we see fuzzy control as a chapter of multi-valued logic programming, this suggests a new and powerful approach to fuzzy control based on positive and negative conditions.

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