一个多值逻辑的一阶谓词系统

鞠实儿曾提出一个开放类三值命题逻辑系统，这一逻辑也可以推广到任意m值逻辑情形，成为一个联结词函数完全的逻辑。本文将对推广的命题逻辑系统L^＊建立一种一阶谓词系统，并证明其可靠性、完全性。

The First Order Predicate Calculus of a Logic System

Ju Shier presented a 3-valued sentential logic system based on open-world assumption. This system can be extended to any finite valued case and become a functional complete system. Because these extended systems are functional complete, all sorts of connectives can be defined in them, such as operators V, A and J. In particular, negation ┐and implication→ can be defined which shows analogy to classical negation ┐and implication→,and they suit for the Rosser-Tuequette conditions. Therefore we can construct a m-valued system L^＊ for each of these extended systems by these defined connectives. After giving the propositional calculus L^＊, we will construct a first order predicate calculus for L^＊ in this paper. The first order predicate system of L^＊ is soundness, and this can be proved easily. The main purpose of this paper is to show the deductive completeness of the order predicate system. For this purpose we construct a maximal consistent set of well-formulas which contains no free variables. We prove the completeness by the method given by Henkin in the 2-valued case.