Normal Form of n-Valued Lukasiewicz Logic Formulas

Abstract

The disjunctive normal form and conjunctive normal form of Boolean functions are very important to construct logic formulas in classical logic system. Shannon expansion in symbolic computation tree logic is generalized to prove the normal form of Boolean functions. In n-valued Lukasiewicz logic system \(L_n\), the expansion of n-valued McNaughton functions which are induced by logic formulas is studied. The quasi disjunctive normal form and quasi conjunctive normal form of m-ary n-valued McNaughton functions are given.