An algebraic method to decide the deduction problem in many-valued propositional calculus
Jinzhao Wu, Hong-yan Tan · 2002
We show that there is a polynomial over the rational number field Q corresponding to a given propositional 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.>