基于正规剩余格的一个逻辑系统及其完备性

A Unified Normal Residuated Based Logic System and Its Completeness

在模糊逻辑中,基于剩余格的逻辑系统起着非常重要的作用.本文提出一种新的代数结构,叫做正规剩余格,研究这种剩余格的性质和结构,建立基于正规剩余格的统一的逻辑系统,许多重要的逻辑系统是这个系统的扩张.进一步。

In fuzzy logic,normal residuated based logic systems play avery important role.In this paper,we propose a kind of new algebraic a kind of new algebraic structure,called normal residuated lattices,study their properties and structure,and construct a unified normal residuated based logic system,which contains many important logic systems as its extensions.Moreover,we discuss the completeness of this unified logic system with respect to the semantics based on normal residuated lattices.