Computing prime implicants/implicates for regular logics

Abstract

Prime implicant/implicate generating algorithms for multiple-valued logics are introduced. Techniques from classical logic not requiring large normal forms or truth tables are adapted to certain "regular" multiple-valued logics. This is accomplished by means of signed formulas, a meta-logic for multiple valued logics; the formulas are normalized in a way analogous to negation normal form. The logic of signed formulas is classical in nature. The presented method is based on path dissolution, a strongly complete inference rule. The generalization of dissolution that accommodates signed formulas is described.<>