Normal modal logic

This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2009)

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.

This logic-related article is a stub. You can help Wikipedia by expanding it. v • d • e