Regular modal logic

In modal logic, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators:

${\displaystyle \Diamond A\leftrightarrow \lnot \Box \lnot A}$

and closed under the rule

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

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

References

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