Philosophy:Regular modal logic

In modal logic, a regular modal logic is a modal logic closed under the duality of the modal operators: $\displaystyle{ \Diamond A \equiv \lnot\Box\lnot A }$

and the rule

$\displaystyle{ (A\land B)\to C \vdash (\Box A\land\Box B)\to\Box C. }$

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.