概率逻辑学基本定理的推广

通过引入生成状态集和生成概率等概念给出了概率逻辑学基本定理的简捷证明,并进一步通过引入自然合并概率的概念将概率逻辑学的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.然后将概率逻辑学的基本方法引入计量逻辑学,得出了带参数 的有限逻辑理论相容度概念,是δ-相容度的推广.

Generalization of Fundamental Theorem of Probability Logic

By introducing the concepts of generating states set and generating probability a simple and direct proof of the fundamental theorem of probability logic is proposed.Next,by introducing the concept of naturally merged probability the fundamental theorem has been generalized.Moreover,the present paper extends the concept of δ -consistency degree of finite logic theories to be the concept of -consistency degree and therefore certain relationship between probability logic and quantitative logic has been obtained.