格值逻辑命题逻辑(L_n×L_2)P(X)中广义文字的α-归结性
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摘要
由于格值逻辑中广义文字结构的复杂性,这必然增加判断两个广义文字是否为α-归结对的难度。根据真值域L_n×L_2的结构特性和归结水平α的特点,研究了真值域为一类格蕴涵代数L_n×L_2的格值命题逻辑系统(L_n×L_2)P(X)中0-IESF与其他广义文字之间的α-归结性,得到了两个广义文字可进行α-归结的条件。
Because of the complexity of generalized literals structure in lattice-valued logic, it leads to difficult to judge two generalized literals whether form resolution pair or not. According to particular structure of truth valued range L_n×L_2 and the characteristic of resolution level α, the resolvability of between 0-IESF and other generalized literals in lattice-valued propositional logic system(L_n×L_2)P( X ) based on one class of lattice implication algebras L_n× L_2, and the determination conditions on that two generalized literals can form resolution pair.
Because of the complexity of generalized literals structure in lattice-valued logic, it leads to difficult to judge two generalized literals whether form resolution pair or not. According to particular structure of truth valued range L_n×L_2 and the characteristic of resolution level α, the resolvability of between 0-IESF and other generalized literals in lattice-valued propositional logic system(L_n×L_2)P( X ) based on one class of lattice implication algebras L_n× L_2, and the determination conditions on that two generalized literals can form resolution pair.
引文
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[15]Xu Yang,Ruan Da,Qin Keyun,et al.Lattice-valued logic:an alternative approach to treat fuzziness and incomparability[M].Berlin:Springer-Verlag,2003.
[16]Xu Yang,Chen Shuwei,Liu Jun,et al.Weak completeness of resolution in a linguistic truth-valued propositional logic[C]//Melin P,Castillo O,Aguilar L T,et al.12th International Fuzzy Systems Association World Congress on Theoretical Advances and Applications of Fuzzy Logic and Soft Computing,Cancun,Mexico,2007:358-366.
[2]刘叙华,姜云飞.定理机器证明[M].北京:科学出版社,1987:84-91.
[3]Xu Yang,Ruan Da,Kerre E E,et al.α-resolution principle based on lattice-valued propositional logic LP(X)[J].Information Sciences,2000,130:195-222.
[4]Xu Yang,Ruan Da,Kerre E E,et al.α-resolution principle based on first-order lattice-valued logic LF(X)[J].Information Sciences,2001,132:221-239.
[5]王伟.格值命题逻辑系统LP(X)中基于α-归结原理的自动推理方法研究[D].成都:西南交通大学,2002.
[6]李文江.基于格蕴涵代数的广义格值模态逻辑及其归结自动推理的研究[D].成都:西南交通大学,2002.
[7]孟丹,徐扬.基于矩阵运算的基于归结原理的自动推理算法[M]//中国人工智能进展.北京:北京邮电大学出版社,2003:172-176.
[8]李晓冰,邱小平,常之艳,等.格值命题逻辑系统中α-归结域与J-归结域的一些性质[J].数学季刊,2008:262-269.
[9]He Xingxing,Xu Yang,Liu Jun.α-input andα-unit resolution methods for generalized horn clause set[J].Journal of Donghua University,2012,28(1):66-70.
[10]Zhang Jiafeng,Xu Yang,He Xingxing.α-resolution fields of generalized literals in lattice-valued propositional logic[J].Journal of Computational Information System,2012,8(18):7543-7552.
[11]Xu Yang,Liu Jun,Zhong Xiaomei,et al.Multiaryα-resolution principle for a lattice-valued logic[J].IEEE Transactions on Fuzzy Systems,2013,21(5):898-912.
[12]Liu Yi,Jia Hairui,Yang Xu.Determination of 3-aryα-resolution in lattice-valued propositional logic LP(X)[J].International Journal of Computational Intelligence Systems,2013,6(5):943-953.
[13]徐扬.格蕴涵代数[J].西南交通大学学报,1993,28(1):20-27.
[14]徐扬,秦克云.格值命题逻辑(I)[J].西南交通大学学报,1993,28(1):123-128.
[15]Xu Yang,Ruan Da,Qin Keyun,et al.Lattice-valued logic:an alternative approach to treat fuzziness and incomparability[M].Berlin:Springer-Verlag,2003.
[16]Xu Yang,Chen Shuwei,Liu Jun,et al.Weak completeness of resolution in a linguistic truth-valued propositional logic[C]//Melin P,Castillo O,Aguilar L T,et al.12th International Fuzzy Systems Association World Congress on Theoretical Advances and Applications of Fuzzy Logic and Soft Computing,Cancun,Mexico,2007:358-366.