基于Gdel蕴涵算子的导出算子的n值逻辑系统  

n-valued logic system Gn based on the derived operator of Gdel implication operator

作　　者：杨春志[1] 李永明[2] 

机构地区：[1]淮南师范学院数学系 [2]陕西师范大学计算机科学学院,陕西西安710062

出　　处：《纺织高校基础科学学报》2008年第1期10-13,共4页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(10571112)

摘　　要：讨论剩余类蕴涵算子之一Gdel蕴涵算子的导出算子的三值系统G3和n值逻辑系统Gn(n>3).给出了G3的真值表,它是C2真值表的扩充,也保持MP规则和正则性.讨论了G3中的重言式(tautology)与IPC(intuitionistic propositional calculus)公理之间的关系以及G3的准重言式与C2的重言式之间的关系.考虑了Gn中的子代数及不同逻辑系统Gn中重言式的比较.One of the residuated class implication operators n-valued logic system （n≥3） based on the derived operator of Godel implication operator is discussed. Firstly, the value table on logic system G3 is given. It is proven that the logic system G3 is a generalization of the classical logic system C2. Secondly, the relation between the tautologies in the logic system G3 and IPC （Intuitionistic propositional calends） axioms, the quasi-tautologies in the logic system G3 and the classical logic system C2 are discussed. At last, the sub-algebra in the logic system Gn is investigated and the relation of the tautologies in some different logic systems Gn is compared.

关 键 词：Godel蕴涵算子 Godel蕴涵算子的导出算子G3 重言式 n值逻辑系统Gn 

分 类 号：O141.1[理学—数学] O159.1[理学—基础数学]