In
modal logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...
, a regular modal logic is a modal logic containing (as axiom or theorem) the
duality of the modal operators:
and closed under the rule
Every
normal modal logic In logic, a normal modal logic is a set ''L'' of modal formulas such that ''L'' contains:
* All propositional tautologies;
* All instances of the Kripke schema: \Box(A\to B)\to(\Box A\to\Box B)
and it is closed under:
* Detachment rule (''modus po ...
is regular, and every regular modal logic is
classical.
References
*Chellas, Brian. ''Modal Logic: An Introduction''. Cambridge University Press, 1980.
Logic
Modal logic
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