Parameterized prime implicant/implicate computations for regular logics
Abstract
Prime implicant/implicate generating algorithms for multiple-valued logics (MVL's) 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. The method is first characterized as a procedure iterated over the truth value domain $\Delta\,=\,\{0,1, \dots ,n-1\}$ of the MVL. The computational requirements are then reduced via parameterization with respect to the elements and the cardinality of $\Delta$.
Full text
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