判定多值逻辑推导问题的代数方法

An Algebraic Method to Decide the Deduction Problem in Multi-Valued Logic

本文证明了对于给定的多值逻辑系统中的命题公式，存在有理数域上的多项式与之对应．从而判定一个命题公式能否以一组命题公式推出，我们只需判定某一多项式是否在一代数簇上消失．通过代数簇的分解，给出了判定这一问题的算法．

We show that there is a polynomial over the rational number field Q corresponding to a given porpositional formula in a given many-valued logic. Then, to decide whether a propositional formula can be deduced from a finite set of such formulas (deduction problem),we only need to decide whether the polynomial vanishes on an algebraic variety which is related to this formula set. By decomposing this algebraic variety . an algorithm to decide this problem is given.