Normal modal logic

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

• L contains:
  • all propositional tautologies ,
  • all instances of the Kripke schema: ${\displaystyle \Box (A\to B)\to (\Box A\to \Box B)}$
• and L is closed under:
  • the mode ponens : , ${\displaystyle A\to B,A\vdash B}$
  • the rule of necessity: implied . ${\displaystyle \vdash A}$ ${\displaystyle \vdash \Box A}$

The smallest logic that meets these conditions is K . The modal logics most commonly used today, e.g. B. CI Lewis ' S4 and S5 , are extensions of K . However, some Deontic and Epistemic Logics are abnormal , often because they abandon the Kripke scheme.

literature

• Ulf Friedrichsdorf : Introduction to classical and dimensional logic . Vieweg, 1992, ISBN 3-528-06489-7 .
• George Edward Hughes , Max Cresswell : Introduction to Modal Logic . De Gruyter, 1978, ISBN 3-11-004609-1 .
• George Edward Hughes, Max Cresswell: A new introduction to modal logic . Routledge, London 1996, ISBN 0-415-12600-2 .