# Classical modal logic

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In modal logic, a **classical modal logic** **L** is any modal logic containing (as axiom or theorem) the duality of the modal operators

which is also closed under the rule

Alternatively one can give a dual definition of **L** by which **L** is classical iff it contains (as axiom or theorem)

and is closed under the rule

The weakest classical system is sometimes referred to as **E** and is non-normal. Both algebraic and neighborhood semantics characterize familiar classical modal systems that are weaker than the weakest normal modal logic **K**.

Every regular modal logic is classical, and every normal modal logic is regular and hence classical.

## References

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