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: .
Moreover, L is closed under:
- Substitution;
- Detachment rule: from A and A→B infer B;
- Necessitation rule: from A infer .
The modal logic with just the above features is called K. Normal modal logic, a proper extension of the propositional calculus, includes most modal logics commonly used nowadays, including C. I. Lewis's S4 and S5.