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: ◻ ( A → B ) → ( ◻ A → ◻ B ) {\displaystyle \Box (A\to B)\to (\Box A\to \Box B)} and it is closed under: Detachment rule (modus ponens): A → B , A ∈ L {\displaystyle A\to B,A\in L} implies B ∈ L {\displaystyle B\in L} ; Necessitation rule: A ∈ L {\displaystyle A\in L} implies ◻ A ∈ L {\displaystyle \Box A\in L} . The smallest logic satisfying the above conditions is called K. Most modal logics commonly used nowadays (in terms of having philosophical motivations), e.g.