Kripke (1965) already introduced “non-normal worlds” for the semantics of modal systems such as C.I. Lewis’ S2 and S3: such worlds were points where all formulas of the form \(\Diamond A\) are true, and all those of the form \(\Box A\) are false (intuitively: everything is possible, nothing is necessary). Cresswell (1970) offered a logic of belief in which beliefs were modelled with sets of both possible and impossible worlds, so as to not treat every impossible belief the same as every other, a