Computer Science ›› 2015, Vol. 42 ›› Issue (Z11): 75-79.

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Theory of Probability Truth Degree in Gdel 4-valued Propositional Logic System

HE Jin-rui, HUI Xiao-jing and SHUANG Jing-ning   

  • Online:2018-11-14 Published:2018-11-14

Abstract: This paper proposed the theory of probability truth degree in Gdel 4-valued propositional logic.It is proved that the set of probability truth degree of all formulas has no isolated point in [0,1].The conceptions of probability similarity degree on two formulas were defined.Moreover,the probability logic metric space was built.It was proved that this space has no isolated point.Then it can provide the thought for approximate reasoning theory.

Key words: Probability truth degree,Similarity degree,Isolated point

[1] 王国俊,傅丽,宋建社.二值命题逻辑中的真度理论[J].中国科学(A辑),2001,31(11):998-1008
[2] 王国俊.数理逻辑引论与归结原理(第二版)[M].北京:科学出版社,2006
[3] 王国俊.计量逻辑学(I)[J].工程数学学报,2006,23(2):191-215
[4] 王国俊,李壁镜.ukasiewicz n值命题逻辑中公式的真度理论和极限定理[J].中国科学(E辑),2005,35(6):561-569
[5] Adams E W.A primer of probability logic[M].Stanford:CSLI Publications,1998
[6] Baioletti M,et al.Simplification rules for the coherent probability assessment problem [J].Ann Math Artif Intell,2002,35:11-28
[7] 李骏,兰倩,黎锁平.ukasiewicz三值命题逻辑中命题的真度理论[J].模糊系统与数学,2004,18(4):39-45
[8] 关晓红,刘晓.ukasiewicz三值命题逻辑系统中公式的概率真度理论[J].计算机工程与应用,2010,46(6):37-41
[9] 关晓红,李骏.标准序列逻辑系统S3中公式的概率真度理论[J].模糊系统与数学,2004,18(4):39-45
[10] Halmos P R.Measure theory[M].New York:Springer-Verlag,1980
[11] 惠小静,王国俊.经典推理模式的随机化研究及其应用[J].中国科学(E辑),2007,37(6):801-812

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