多值逻辑定理机器证明的代数方法

ALGEBRAIC METHODS FOR MECHANICAL THEOREM PROVING IN MANY-VALUED LOGICS

由给定的多值逻辑系统中的一组公式，．．．，，出发，构造出了一组有理数域上的多项式ＰＳ，使得是，．．．，的逻辑结论，当且仅当ＰＳ定义的代数簇为空集，当且仅当ＰＳ生成的理想是平凡理想．从而，利用特征列方法和Ｇｒｏｅｂｎｅｒ基方法，给出了判定是否，．．．，逻辑结论的两种算法．

A polynomial system PS over the rational number field is constructed from the formula...,in a given many-valued logic system such that follows from ...,iff the algebraic variety defined by PS is empty, iff the idealenerated by PS is trivial. Two algorithms to decide whether follows from,...,are thus developed by employing characteristic set method and Groebner basismethod.