Left-distributivity over $\lor$: $P \star (Q \lor R) \equiv (P \star Q) \lor (P \star R)$

Commutativity: $P \star Q \equiv Q \star P$

Associativity: $(P \star Q) \star R \equiv P \star (Q \star R)$

Right-distributivity over $\lor$: $(Q \lor R) \star P \equiv (Q \star P) \lor (R \star P)$