Regular modal logic

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In modal logic, a regular modal logic L is a modal logic closed under the duality of the modal operators:

\Diamond A \equiv \lnot\Box\lnot A

and the rule

(A\land B)\to C \vdash (\Box A\land\Box B)\to\Box C.

Every regular modal logic is classical, and every normal modal logic is regular and hence classical.


Chellas, Brian. Modal Logic: An Introduction. Cambridge University Press, 1980.