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| Random Truth Theory of Proposition Logic and Its Application |
| LIU Xiao-Ling1,ZHANG Jia-Lu2 |
1. Department of Computer Science,Xiangnan University,Chenzhou 423000
2.Department of Mathematics,Xiangnan University,Chenzhou 423000 |
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Abstract In this paper,the concept of random truth degree of proposition formulas based on a random variable sequence is introduced,which is a common generalization of various concepts of truth degree existing in references,and the set of random truth degree of all logic formulas is proved to have no isolated point in [0,1]. The random similarity degree and random pseudo-metric space between two logic formulas are defined by means of random truth degrees,and the random logic pseudo-metric space is proved to have no isolated point. The random truth degree of proposition logic is a generation of various truth degree of proposition logic. Using convergence theorem of integration in probability,a limit theorem of truth degrees is given,which shows the connection of various truth degrees. Various logic operations are continuous in random logic pseudo-metric space,and the fundamental theorem of probability logic is extended to the multi-valued proposition logic. Two diverse approximate reasoning ways are proposed in random logic pseudo-metric space.
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Received: 12 March 2011
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