Normal modal logic

A normal modal logic is the logic of a set L of modal formulas, so that

  • L contains the following: all propositional tautologies
  • All instances of the Kripke schema:
  • The modus ponens:
  • The Necessity rule implies.

The smallest logic that satisfies these conditions is called K. The modal logics most commonly used today, for example, CI Lewis' S4 and S5, are extensions of K. However, some deontic and epistemic logics non-normal, often because they quit Kripke schema.

Tautology (logic) Clarence Irving Lewis Deontic logic Epistemic modal logic George Edward Hughes
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