Lukasiewicz命题逻辑系统中真度的等价定义及相关性质  

An Equivalent Definition and Some Properties of Truth Degrees in Lukasiewicz Proposition Logic System

作　　者：周建仁[1] 吴洪博[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》2013年第4期580-590,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11171196)~~

摘　　要：对Lukasiewicz命题逻辑系统中的公式真度理论进行了研究.首先,给出了Lukasiewiczn值命题逻辑系统中一个更为直观的真度定义的等价形式;其次,利用真度定义的等价形式简化了连接Lukasiewiczn值命题逻辑系统和Lukasiewicz连续值命题逻辑系统中真度理论的极限定理的证明;第三,得到了真度性质:在Lukasiewicz逻辑系统中,把命题公式中的原子命题与该原子命题的否定互换,公式的真度不变;第四,讨论了真度与推理规则之间的关系,给出了Lukasiewicz命题逻辑系统中真度与MP规则的精确关系式以及关于真度并推理规则的结果.The theory of truth degrees in the Lukasiewicz proposition logic system is investigated in this paper. Firstly, an intuitionistic equivalent form of the definition of truth degrees in the Lukasiewicz n-valued proposition logic system is given; Secondly, the proofs of the limit theorem that connect the theory of truth degrees of Lukasiewicz n-valued proposition logic sys- tern and Lukasiewicz continuity-valued is simplified through the equivalent form of definition; Thirdly, it is proved that the truth degree of a formula keeps invariability when an exchange takes place among its atomic formula and the negation; Fourthly, the relationship between inference rules and truth degrees is discussed. A precise equation about MP rule and truth degrees is obtained, and the consequence about the union inference rule of truth degrees is also obtained in Lukasiewicz proposition logic system.

关 键 词：计量逻辑学 Lukasiewicz命题逻辑 真度定义 等价形式 推理规则 

分 类 号：O141.1[理学—数学]