Logic Systems

System T

(1) □ p → p

(2) □ (p → q) → (□ p → □ q)

System B (Brouwerian)

(3) p → □ ◊ p

System S4 (Lewis)

(4) □ p → □ □ p

System S5 (Lewis)

(5) ◊ p → □ ◊ p