Lukasiewicz命题逻辑系统中真度的等价定义及相关性质

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 system 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.