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A Unified Normal Residuated Based Logic System and Its Completeness

PEI Dao-wu (Department of Mathematics, Yancheng Teachers College, Yancheng 224002, China)  
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.
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