Regular modal logic explained

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

\Diamond A \leftrightarrow ln ot\Box ln ot A

and closed under the rule

((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.