 In impossible worlds semantics, different impossibilities can be distinguished by being associated with different sets of worlds (only impossible worlds), and different necessary truths can also be distinguished by different sets of worlds (all possible worlds plus some of the impossible worlds). Each distinct necessary truth will correspond to a distinct set containing all possible worlds and some impossible worlds; and each distinct impossible proposition will correspond to a set of worlds that contains no possible worlds, but which may contain impossible worlds (Rantala 1982).