The method of polynomial ring calculus and its potentialities

This paper surveys some results on the role of formal polynomials as a representation method for logical derivation in classical and non-classical logics, emphasizing many-valued logics, paraconsistent logics and non-deterministic logics, as well as their potentialities for alternative algebraic representation and for automation. The resulting mechanizable proof method exposed here is of interest for automatic proof theory, as the proof methods are comparable to analytic tableaux in generality and intuitiveness, and seems also to indicate a new avenue for investigating questions on complexity.