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date: 21 January 2018

modal logic

A Dictionary of Logic

Thomas Macaulay Ferguson,

Graham Priest

modal logic 

A modal logic is a logic which deals with the modalities of necessity and possibility. Such a logic was first formulated in Aristotle’s syllogistic and was investigated by medieval logicians. In its modern form, modal logic was developed by the logican Clarence Irving Lewis (1883–1964), who was motivated by the paradoxes of relevance. He produced five systems of logic, modal logicmodal logic. These were formulated purely axiomatically. Semantics for these logics were later developed by several people, but principally by Saul Kripke with Kripke semantics. It then became clear that Lewis’ systems were just five of an infinite number of such logics, and that the most basic of these, modal logic, was none of the Lewis systems.