Affiliations: Department of Mathematics, Xiangnan University, Chenzhou, Hunan, China | Department of Computer Science, Xiangnan University, Chenzhou, Hunan, China
Note: [] Corresponding author. Jialu Zhang, Department of Mathematics, Xiangnan University, Chenzhou, Hunan 423000, China. Tel.: +86 18973579659; E-mail: zjl0735@163.com
Abstract: In this paper, we introduce the concept of random truth degree of an abstract proposition, which is a common generalization of various concepts of truth degree existing in literature, and prove that the set of random truth degree of all propositions has no isolated points in the real unit interval I = [0, 1]. We define random resemblance degree and random logic pseudo-metric among two propositions by means of random truth degrees, and prove that the random logic pseudo-metric space has no isolated points. By virtue of integral convergence theorem in probability theory we give a limit theorem of random truth degrees, which shows the connection of various truth degrees existing in literature. As an application we propose two diverse approximate reasoning models in random logic pseudo-metric space.
Keywords: Propositional logic, random truth degree, random resemblance degree, random logic pseudo-metric space, approximate reasoning
