Normal modal logic

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In logic, normal modal logic is a set L of modal formulas such that L contains

  • all propositional tautologies,
  • Kripke's schema: <math>\Box(A\to B)\to(\Box A\to\Box B)</math>,

and L is closed under

  • substitution,
  • detachment rule: from A and A→B infer B,
  • necessitation rule: from A infer <math>\Box A</math>.

The minimal normal modal logic is known as K.

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