The modalities of truth They are (informal) definitions, so their true is established a priori.
I want to say that a "unnecessary" conclusion can be "invalid" in two ways ("possibly" and "impossibly" true). MP inference is a valid scheme (necessary), AC is invalid but "possible" and MT asymmetric (to infer "A") is "impossible" to be true.
If something is not necessary, then it is contingent; if contingent, it can be possible and impossible. If it possible, also it can be "real" or "empirically" true.