If we prove that ∀w((w,A) fo →(w,B) fo ), we know that B is not informative with respect to A.
if we are able to show that both ∃w((w,A) fo ∧ (w,B) fo ) and ∃w((w,A) fo ∧ ¬(w,B) fo ) are satisfiable formulas, we can say that B is informative with respect to A.