Kleene蕴涵算子的导出算子的n值逻辑系统I_n  

n-valued Logic System I_n Based on the Derived Operator of Kleene Implication Operator

作　　者：程贞敏[1] 尤飞[1] 李洪兴[1] 

机构地区：[1]北京师范大学数学科学学院,北京100875

出　　处：《模糊系统与数学》2005年第1期18-21,共4页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目 (6 0 4 74 0 2 3) ;教育部博士点基金资助项目 (2 0 0 2 0 0 2 70 13) ;教育部科学技术重点资助项目 (0 3184 ) ;973国家重点基础研究发展规划基金资助项目 (2 0 0 2 CB312 2 0 0 )

摘　　要：考虑了Kleene蕴涵算子的导出算子的三值逻辑系统I3 和n值逻辑系统In(n >3)。首先,给出I3的真值表,证明了I3 是二值逻辑系统C2 的推广。其次,讨论了I3 中的重言式与IPC公理之间以及I3 中的准重言式与C2 中的重言式之间的关系。接着,考虑了In中的子代数。最后。n-valued logic system (n≥3) based on the derived operator of Kleene implication operator is considered. Firstly, the true-value table on logic system I_(3) is given. It is proved that the logic (system) I_(3) is a generalization of the classical logic system C_(2). Secondly, the relation between the (tautologies) (in the) logic system I_(3) and IPC axioms, the quasi-tautologies in the logic system I_3 and the tautologies in the classical logic system C_2 are discussed. Thirdly, the sub-algebra in the logic (system) I_(n) is (investigated.) At last, the relation of tautologies in some different logic systems I_(n) are researched.

关 键 词：Kleene蕴涵算子 Kleene蕴涵算子的导出算子 n值逻辑系统In 准重言式 重言式 

分 类 号：O159.1[理学—数学] O141.1[理学—基础数学]