 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, and to allow someone to believe some necessary truths without believing them all. (See also Hintikka 1975). Since then, impossible worlds have been used to theorize about many of the hyperintensional phenomena discussed in this entry.