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.
刘晓玲，张家录. 命题逻辑的随机真度理论及其应用[J]. 模式识别与人工智能, 2013, 26(3): 231-241.
LIU Xiao-Ling,ZHANG Jia-Lu. Random Truth Theory of Proposition Logic and Its Application. , 2013, 26(3): 231-241.
[1] #Shi Chunyi,Huang Changning,Wang Jiaqin. Principle of Artificial Intelligence. Beijing,China: Tsinghua University Press,1993 (in Chinese) (石纯一,黄昌宁,王家钦.人工智能原理.北京:清华大学出版社,1993) [2] Lu Ruqian,Ying Minsheng. A Model of the Knowledge Based Reasoning. Science in China: Series E,1998,28(4): 363- 369 (in Chinese) (陆汝钤,应明生.知识推理的一个模型.中国科学:E辑,1998,28(4): 363-369) [3] 2Lioyd J W. Foundations of Logic Programming. New York: Springer Verlag,1987 [4] Hájek P. Metamathematics of Fuzzy Logic. Norwell,USA: Kluwer Academic Publisher,1998 〖HJ*5/8[5] Wang Guojun. Non Classical Logic and Approximate Reasoning. Beijing,China: Science Press,2000 (in Chinese) (王国俊.非经典数理逻辑与近似推理.北京:科学出版社,2000) [6] Wang Guojun. Mathematical Logic and Principle of an Attribute. 2nd Edition. Beijing,China: Science Press,2006 (in Chinese) （王国俊.数理逻辑引论与归结原理.第2版.北京:科学出版社,2006） [7] Wang Guojun. Quantitative logic I. Chinese Journal of Engineering Mathematics,2006,23(2): 191-215 (in Chinese) (王国俊.计量逻辑学I.工程数学学报,2006,23(2): 191-215) [8] 2Wang Guojun. Fully Implication Triple I Method of Fuzzy Reasoning. Science in China: Series E,1999,29(1): 43-53 (in Chinese) (王国俊.模糊推理的全蕴涵三I算法.中国科学:E辑,1999,29(1): 43-53) [9] Wang Guojun,Wang Wei. Logic Metric Spaces. Acta Mathematica Sinica,2001,44(1): 159-168 (in Chinese) (王国俊,王 伟.逻辑度量空间.数学学报,2001,44(1): 159-168) [10] Wang Guojun,Fu Li,Song Jianshe. Theory of Truth Degrees of Propositions in Two Valued Logic. Science in China: Series A,2001,31(11): 998-1008 (in Chinese) (王国俊,傅 丽,宋建社.二值命题逻辑中命题的真度理论.中国科学:A辑,2001,31(11): 998-1008) [11] Wang Guojun,Li Bijing. Theory of Truth Degrees of Formulas in Lukasiewicz n Value Propositional Logic and a Limit Theorem. Science in China: Series E,2005,35(6): 561-569 (in Chinese) (王国俊,李壁镜.Lukasiewicz n值命题逻辑中公式的真度理论和极限定理.中国科学:E辑,2005,35(6): 561-569) [12] Li Jun,Wang Guojun. Theory of Truth Degrees of Propositions in Logic System L*n. Science in China: Series E,2006,36(6): 631-643 (in Chinese) (李 骏,王国俊. 逻辑系统Ln中命题的真度理论.中国科学:E辑,2006,36(6): 631-643) [13] Hui Xiaojin,Wang Guojun. Randomization of Classical Inference Patterns and the Application. Science of China: Series E,2007,37(6): 801-812 (in Chinese) (惠小静,王国俊.经典推理模式的随机化研究及其应用.中国科学:E辑,2007,37(6): 801-812) [14] Adams E W. A Primer of Probability Logic. Stanford: CSLI Publications,1998 [15] Wang Guojun,Hui Xiaojing. Generalization of Fundamental Theorem of Probability Logic. Acta Electronica Sinica,2007,35(7): 1333-1340 (in Chinese) (王国俊,惠小静.概率逻辑学基本定理的推广.电子学报,2007,35(7): 1333-1340) [16] Yan Shijian,Wang Junran,Liu Xiufan. Foundations of Probability Theory. Beijing,China: Science Press,1985 (in Chinese) (严士健,王隽骧,刘秀芳.概率论基础.北京:科学出版社,1985) [17] Halmos P R. Measure Theory. New York,USA: Spring Verlag,1974
2013, Vol. 26 
