branch of logic that deals with modalities (such properties of propositions as necessity, contingency, possibility, and impossibility), as opposed to truth and falsity; thus the statements “Some men may be immortal” and “Men are necessarily social animals” are modal propositions. Although modal syllogisms were considered by Aristotle, modal logic remains today an uncertain field. Modern attempts to deal with the problem are found in the many-valued logics, which allow other truth-values between truth and falsity, and in systems of strict implication—systems of theorems that differ somewhat depending upon the relations between the different modalities that are set forth in their axioms. Compare truth-value.