Generalized Root of Theories in Propositional Fuzzy Logical Systems

摘要

In order to study the logic foundation of fuzzy reasoning and the construction rnof the sets D(Γ) , this paper first put forth a definition of generalized root of theoretic in Lukasiewicz propositional fuzzy logic system, Goedel propositional fuzzy logic system, product propositional fuzzy logic system,and the R_O-propositional fuzzy logic system. Then it goes on to prove that D(Γ) is completely determined by its generalized root whenever theory Γ has a generalized root, thereafter it puts forward the construction of D(Γ). Finally, it argues that every finite theory Γ has a generalized root, which can be expressed in some specific form, and that there does exist certain relationship between different theory Γ.