# Normal modal logic

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In logic, a **normal modal logic** is a set *L* of modal formulas such that *L* contains:

- All propositional tautologies;
- All instances of the Kripke schema:

and it is closed under:

- Detachment rule (Modus Ponens): ;
- Necessitation rule: implies .

The smallest logic satisfying the above conditions is called **K**. Most modal logics commonly used nowadays (in terms of having philosophical motivations), 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.