Many-Valued Propositional Calculi

Abstract

The origins of multivalued logics can be traced as deep as the treatises of Aristotle. He was the first to object to rigid bivalence of statements. His doubts concerned the so-called Law of the Excluded Middle (p V ~ p), considered as undeniable truth in classical logic. The idea of accepting sentences which (in a given instance) fail to be either absolutely true or absolutely false aroused contention between the Epicureans, on the one side, and the Stoics (including Chrysippus) on the other. The latter represented the standpoint of extreme determinism, with its orthodox bivalence in logic. The former, rejecting absolute determinism, admitted the possibility that neither of two statements, one of which negated the other, must necessarily be true; in particular, when the statements involved events that were to come. This is the reason why many-valued logics (or, more generally, non-classical logics) are sometimes referred to as non-Chrysippean.