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: [math]\displaystyle{ \Diamond A \leftrightarrow \lnot\Box\lnot A }[/math]

and closed under the rule

[math]\displaystyle{ \frac{(A\land B)\to C}{(\Box A\land\Box B)\to\Box C}. }[/math]

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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