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.

### Other articles related to "modal logic, logics, modal, logic, modal logics":

... Two of Kripke's earlier works, A Completeness Theorem in

**Modal Logic**and Semantical Considerations on

**Modal Logic**, the former written while he was still a teenager, were on the subject of

**modal logic**... The most familiar

**logics**in the

**modal**family are constructed from a weak

**logic**called K, named after Kripke for his contributions to

**modal logic**... semantics (also known as relational semantics or frame semantics) for

**modal logics**...

### Famous quotes containing the words logic and/or normal:

“The much vaunted male *logic* isn’t logical, because they display prejudices—against half the human race—that are considered prejudices according to any dictionary definition.”

—Eva Figes (b. 1932)

“Normality highly values its *normal* man. It educates children to lose themselves and to become absurd, and thus to be *normal*. *Normal* men have killed perhaps 100,000,000 of their fellow *normal* men in the last fifty years.”

—R.D. (Ronald David)