Philosophy: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: $◊A\leftrightarrow \mathrm{\neg }◻\mathrm{\neg }A$

and closed under the rule

$\frac{(A\wedge B)\to C}{(◻A\wedge ◻B)\to ◻C}.$

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

References

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