Regular modal logic

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.

References

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