Polynomial ring calculus for many-valued logics

Abstract

This paper discusses a new algebraic proof method for general sentential logics, which is particularly apt for finitely-many-valued logics and for PC, based on reducing polynomials over finite fields. The method can also be extended to cover certain non-finitely valued logics and non-truth-functional logics as well, provided they can be characterized by two-valued dyadic semantics. The resulting mechanizable proof method introduced here is of interest for automatic proof theory, and seems also to be appropriate for investigating questions on complexity.