Lukasiewicz命题逻辑中公式的Γ-真度理论和极限定理

The theory of Γ-truth degrees of formulas and limit theorem in Lukasiewicz propositional logic

对"Lukasiewicz n值命题逻辑中公式的真度理论和极限定理"进行了再研究.(1)在Lukasiewicz n值命题逻辑中,给出了真度的赋值表示形式,该形式从赋值角度直接反映了公式的真度表示公式为重言式的隶属度的实质;(2)在Lukasiewicz n值命题逻辑中,利用真度的赋值表示形式提出了公式关于局部有限理论Γ的Γ-真度概念,给出了公式的Γ-真度的几种等价形式及性质;(3)得到了Lukasiewicz n值命题逻辑中关于Γ-真度理论的极限定理;(4)给出了Lukasiewicz连续值命题逻辑中公式的Γ-真度定义的合理形式,以及Lukasiewicz命题逻辑中真度的对称性定理;(5)在Lukasiewicz n值命题逻辑中,利用极限方法和Γ-真度的赋值形式对公式关于无限理论Γ的Γ-真度问题进行了讨论.

The theory of truth degrees of formulas and limit theorem in Lukasiewicz n-valued propositional logic has been investigated again.(1) In Lukasiewicz n-valued propositional logic, a form of truth degree's definition 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 Lukasiewicz n-valued propositional logic, a concept ofΓ-truth degree of a formula relative to locally finite theory Γ is proposed through the valuation's form of truth degree, some equivalent forms with properties of Γ-truth degrees are given;(3) The limit theorem about Γ-truth degree in Lukasiewicz nvalued propositional logic is proved;(4) A reasonable form of Γ-truth degree in Lukasiewicz continuity-valued propositional logic and a symmetrical theorem of truth degree in Lukasiewicz propositional logic are given;(5) In Lukasiewicz n-valued propositional logic, the problem of Γ-truth degrees of formulas relative to infinite theory is discussed by limit method and the valuation's form of Γ-truth degrees.