随机模糊环境下的命题逻辑真度理论*

在实单位区间0,1]具有一定概率分布的基础上,引入命题逻辑公式的随机模糊意义下的真度概念,指出随机真度是已有文献中各种命题逻辑真度的共同推广.利用随机模糊真度定义公式间的随机模糊相似度,导出全体公式集上的一种伪距离——随机模糊逻辑伪距离,证明在随机模糊逻辑伪距离空间无孤立点.利用概率论中的积分收敛定理,证明一个关于随机模糊真度的极限定理.研究已有各种真度之间的联系.证明随机逻辑伪距离空间中逻辑运算的连续性,并将概率逻辑学基本定理推广至多值命题逻辑.在随机逻辑伪距离空间中提出2种不同类型的近似推理模式并应用于实际问题的近似推理.

Truth Theory of Proposition Logic under Random Fuzzy Environment

The concept of random fuzzy truth degree of logic formulas is proposed by virtue of probability distribution on real unit interval 0,1] . It is pointed out that the random fuzzy is the common spread of truths in the valuation domain of logic formulas. Then, the concept of random fuzzy similarity degree between two logic formulas is proposed from the concept of random fuzzy truth degree. Based on it, the pseudo-metric named random fuzzy pseudo-metric is introduced on all formula sets. And it is proved that there are not isolated points in the random fuzzy logic pseudo-metric space. Moreover, by using of the integral convergence theorem in probability theory, a limit theorem of random truth degree is proved. The connection of truth degrees is illustrated by this limit theorem. Furthermore, the continuity of the logical operation in the random logic pseudo-metric space is certified and the fundamental theorems of probabilistic logic are expanded to multi-valued propositional logic. Finally, two kinds of approximate reasoning models are presented and applied to approximate reasoning of the practical problems in random logic pseudo-metric space.