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.

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