Representing Propositional Logic Connectives With Modular Polynomials

This paper explores the relationship between n-valued propositional logic connectives and modular polynomials. Namely the representing of logic connectives using modular polynomials. The case for n = 2 is explored and a method is developed for finding the coefficients of the unique polynomial that represents any given binary logic connective. Examples are then given for using the modular polynomial representations of connectives to determine the validity of propositional arguments. A similar procedure is shown for when n = 3 and an evaluation of the axioms of Łukasiewicz’s 3-valued logic is given using modular polynomials. The general case is explored to determine for which values of n the representation holds. It is then shown that mod n polynomial functions are sufficient for representing any n-valued logic connective if and only if n is prime.