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 ↔ ¬ ◻ ¬ A {\displaystyle \Diamond A\leftrightarrow \lnot \Box \lnot A}

and closed under the rule

( A ∧ B ) → C ( ◻ A ∧ ◻ B ) → ◻ C . {\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

[edit]

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

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