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.
Fund:Supported by Natural Science Foundation of Hunan Province(No.2017JJ2241,16JJ6138), Social Sciences Fund Project of Hunan Province(No.16YBA329), Key Science Research Project of Education Department of Hunan Province(No.2014A135,13A093), Scientific Research Project of Xiangnan University(No.2014XJ54), Construction Program of Key Discipline in Hunan Province
About author:: (WU Xia, born in 1978, master, associate professor. Her research interests include non-classical mathematical logics and approximate reasoning theory.) (ZHANG Jialu(Corresponding author), born in 1964, master, professor. His research interests include non-classical mathematical logics, approximate reasoning theory and intelligent information processing theory.)
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2017, Vol. 30 
