Łukasiewicz 命题逻辑中公式的Γ-真度理论和极限定理

The theory of truth degrees of formulas and limit theorem in Łukasiewicz n-valued propositional logic has been investigated again. (1) In Łukasiewicz n-valued propositional logic, a form of truth degrees de nition described by valuations is given which indicates directly from the aspects of valuations that the truth degree of a formula is membership degree for the formula belonging to tautologies; (2) In Łukasiewicz n-valued propositional logic, a concept of Γ-truth degree of a formula relative to locally nite theory Γ is proposed through the valuations form of truth degree, some equivalent forms with properties of Γ-truth degrees are given; (3) The limit theorem about Γ-truth degree in Łukasiewicz nvalued propositional logic is proved; (4) A reasonable form of Γ-truth degree in Łukasiewicz continuity-valued propositional logic and a symmetrical theorem of truth degree in Łukasiewicz propositional logic are given; (5) In Łukasiewicz n-valued propositional logic, the problem of Γ-truth degrees of formulas relative to in nite theory is discussed by limit method and the valuations form of Γ-truth degrees.