Abstract：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.
吴霞， 张家录. 随机模糊环境下的命题逻辑真度理论*[J]. 模式识别与人工智能, 2017, 30(4): 289-301.
WU Xia, ZHANG Jialu. Truth Theory of Proposition Logic under Random Fuzzy Environment. , 2017, 30(4): 289-301.
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