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In logic, a normal modal logic is a set L of modal formulas such that L contains:
and it is closed under:
The smallest logic satisfying the above conditions is called K. Most modal logics commonly used nowadays , e.g. C. I. Lewis's S4 and S5, are extensions of K. However a number of deontic and epistemic logics, for example, are non-normal, often because they give up the Kripke schema.
Every normal modal logic is regular and hence classical.
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