regular modal logic
modal logic containing the duality axiom schema ◊A↔¬◻¬A as well as the deduction rule (A∧B)→C ⊢ (◻A∧◻B)→◻C
normal modal logic
set of modal formulas containing all propositional tautologies and all instances of the Kripke schema ◻(A→B)→(◻A→◻B) and closed under modus ponens and necessitation