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In modal logic, a regular modal logic is a modal logic closed under the duality of the modal operators:

◊ A ≡ ¬ ◻ ¬ A {\displaystyle \Diamond A\equiv \lnot \Box \lnot A}

and the rule

→ C ⊢ → ◻ C . {\displaystyle \to C\vdash \to \Box C.}

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