逻辑理论的随机相容度
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摘要
在n值Lukasiewicz命题逻辑系统中,提出理论的随机相容度的概念,并指出理论的随机相容度是和概率分布列的选取相关的。最后证明了理论的随机相容度在n值随机逻辑度量空间中,同样保持经典逻辑度量空间中的基本性质。
Randomized consistency degree is introduced in n-valued Lukasiewicz proposition logic system. It is indicated that the randomized consistency degree of a theory is related with the selection of probability distribution. Then it proves that the randomized consistency degree of a theory can maintain the basic properties in n-valued randomized logic metric space as in classical logic metric space.
Randomized consistency degree is introduced in n-valued Lukasiewicz proposition logic system. It is indicated that the randomized consistency degree of a theory is related with the selection of probability distribution. Then it proves that the randomized consistency degree of a theory can maintain the basic properties in n-valued randomized logic metric space as in classical logic metric space.
引文
[1]Wang G J,Zhang W X.Consistency degrees of finite theories in lukasiewicz propositional fuzzy logic[J].Fuzzy Sets and Systems,2005,149:275-284.
[2]Zhou X N,Wang G J.Consistency degrees of theories in some systems of propositional logic[J].Fuzzy Sets and Systems,2005,152:321-331.
[3]Zhou H J,Wang G J.A new theory index based on deduction theorems in several logic systems[J].Fuzzy Sets and Systems,2006,157:427-443.
[4]惠小静,李宏设,李丽.D-逻辑度量空间中的相容理论[J].模糊系统与数学,2009,23(2):12-17.
[5]李修清,吴果林.ξ-逻辑度量空间中理论的开放度[J].桂林航天工业学院学报,2014,19(2):152-155.
[6]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.
[7]惠小静,王国俊.经典推理模式的随机化研究及其应用(II)[J].模糊系统与数学,2008,22(3):21-26.
[8]惠小静.三值R0命题逻辑系统的随机化[J].应用数学学报,2009,32(1):19-27.
[9]惠小静,王国俊.D-逻辑度量空间与近似推理[J].南京大学学报数学半年刊,2007,24(2):249-257.
[10]李修清,魏海新,林亮.修正的n值G?del逻辑系统的随机化[J].计算机工程与应用,2012,48(24):45-49.
[11]李修清,朱宁.R0型命题逻辑系统的随机化[J].模糊系统与数学,2013,27(1):63-70.
[12]李修清,魏海新.n值Lukasiewicz逻辑系统中理论的随机发散度[J].模糊系统与数学,2013,27(6):93-98.
[13]王国俊.数理逻辑引论与归结原理[M].2版.北京:科学出版社,2006.
[14]王国俊.非经典数理逻辑与近似推理[M].2版.北京:科学出版社,2008.
[15]Hamilton A G.Logic for mathematicians[M].New York:Cambridge University Press,1978.
[2]Zhou X N,Wang G J.Consistency degrees of theories in some systems of propositional logic[J].Fuzzy Sets and Systems,2005,152:321-331.
[3]Zhou H J,Wang G J.A new theory index based on deduction theorems in several logic systems[J].Fuzzy Sets and Systems,2006,157:427-443.
[4]惠小静,李宏设,李丽.D-逻辑度量空间中的相容理论[J].模糊系统与数学,2009,23(2):12-17.
[5]李修清,吴果林.ξ-逻辑度量空间中理论的开放度[J].桂林航天工业学院学报,2014,19(2):152-155.
[6]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.
[7]惠小静,王国俊.经典推理模式的随机化研究及其应用(II)[J].模糊系统与数学,2008,22(3):21-26.
[8]惠小静.三值R0命题逻辑系统的随机化[J].应用数学学报,2009,32(1):19-27.
[9]惠小静,王国俊.D-逻辑度量空间与近似推理[J].南京大学学报数学半年刊,2007,24(2):249-257.
[10]李修清,魏海新,林亮.修正的n值G?del逻辑系统的随机化[J].计算机工程与应用,2012,48(24):45-49.
[11]李修清,朱宁.R0型命题逻辑系统的随机化[J].模糊系统与数学,2013,27(1):63-70.
[12]李修清,魏海新.n值Lukasiewicz逻辑系统中理论的随机发散度[J].模糊系统与数学,2013,27(6):93-98.
[13]王国俊.数理逻辑引论与归结原理[M].2版.北京:科学出版社,2006.
[14]王国俊.非经典数理逻辑与近似推理[M].2版.北京:科学出版社,2008.
[15]Hamilton A G.Logic for mathematicians[M].New York:Cambridge University Press,1978.