View your list of saved words. (You can log in using Facebook.)
Formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. The most straightforward way of constructing a modal logic is to add to some standard nonmodal logical system a new primitive operator intended to represent one of the modalities, to define other modal operators in terms of it, and to add axioms and/or transformation rules involving those modal operators. For example, one may add the symbol L, which means It is necessary that, to classical propositional calculus; thus, Lp is read as It is necessary that p. The possibility operator M (It is possible that) may be defined in terms of L as Mp = ¬L¬p (where ¬ means not). In addition to the axioms and rules of inference of classical propositional logic, such a system might have two axioms and one rule of inference of its own. Some characteristic axioms of modal logic are: (A1) Lp p and (A2) L(p q) (Lp Lq). The new rule of inference in this system is the Rule of Necessitation: If p is a theorem of the system, then so is Lp. Stronger systems of modal logic can be obtained by adding additional axioms. Some add the axiom Lp LLp; others add the axiom Mp LMp.
This entry comes from Encyclopædia Britannica Concise. For the full entry on modal logic, visit Britannica.com.
Seen & Heard
What made you look up modal logic? Please tell us what you were reading, watching or discussing that led you here.