概率逻辑中的命题相关性与逻辑运算

Proposition relativity and logic calculation in probabilistic logic

原子命题是数理逻辑研究的基本单位.分析了原子命题的相关性与逻辑运算之间的关系.在经典二值逻辑中,命题逻辑运算结果的真值只与参与运算的命题的真值有关,而与命题的具体内容无关;在概率逻辑中,命题逻辑运算由命题的关系决定,真值相同的不同命题,逻辑运算结果不一定相同.定义了与经典二值逻辑相容的蕴涵联结词,克服了条件概率不能用于推理的缺点.

Atom propositions are the basic unit of symbolic logic. The relationship between atom propositions＇ relativity and logic calculation was analyzed. In classical two-valued logic, the truth value of the proposition logic calculation result only bears on the truth value of the proposition which participates in the logic calculation, but is independent of the idiographic content in the proposition. In probabilistic logic, proposition logic calculation is decided by the relationship of propositions. The different propositions with the same truth value can not have the same logic calculation result. Implication connectives which are compatible with classical two-valued logic were defined, and they overcome the shortcoming that conditional probability can not be used to inference.