概率逻辑学基本定理在多值命题逻辑系统中的推广

Generalization of Fundamental Theorem of Probability Logic in Multi-valued Propositional Logic

通过引入概率测度空间,在n值Lukasiewicz命题逻辑系统中提出了满足Kolmogorov公理的命题公式的概率;证明了概率逻辑学基本定理,并将概率逻辑学基本定理推广到了更一般的形式,改进了对推理结论的不可靠度上界的估计;将概率逻辑学的基本方法引入计量逻辑学,建立了更一般的逻辑度量空间;通过概率逻辑学基本定理,证明了逻辑度量空间中概率MP,HS规则,它是真度MP,HS规则的推广.

By means of probability measure space,the concept of probability which satisfied Kolmogorov axioms is introduced in n-valued Lukasiewicz logical system.The fundamental theorem of probability logic is proved and generalized in n-valued Lukasiewicz logical system,so the estimate of uncertainty of conclusions in inference is improved.The basic methods of probability logic are introduced into quantitative logic and a more general logic metric space has been obtained;The MP、HS rules of probability are proved by the fundamental theorem of probability logic,and it is the generalization of the MP、HS rules of truth.