Normal Modal Logic

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":

Saul Kripke - Modal Logic
... 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 ...

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