  The notion of correspondence between axioms and frame conditions that is at issue here was explained in the previous section. When S is a list of axioms and F(S) is the corresponding set of frame conditions, then S corresponds to F(S) exactly when the system K+S is adequate (sound and complete) for F(S)-validity, that is, an argument is provable in K+S iff it is F(S)-valid. Several stronger notions of correspondence between axioms and frame conditions have emerged in research on modal logic. 