命题中介逻辑的可靠和完备Gentzen推导系统

Sound and Complete Gentzen Deduction System for Intermediate Propositional Logic

中介逻辑是朱梧槚先生提出的一个3-值逻辑.给出了一个命题中介逻辑,其中引入中介连接词-、反对连接词 以及蕴涵连接词→,并且定义否定连接词.给出了一个Gentzen-型的推导系统,使得该系统关于中介逻辑的3-值语义是可靠的和完备的.

The intermediate logic is a three-valued logic proposed by Zhu Wu-Jia. A propositional intermediate logic is proposed in this paper where the intermediate unary connective - and the contrary connective are introduced, and the negative connective is defined in terms of the unique binary connective → A Gentzen-typed deduction system is given such that the system is sound and complete with the three-valued semantics of the propositional intermediate logic.