 Carnap’s semantics is indeed a precursor of Possible Worlds Semantics (PWS). Yet some crucial ingredients are still missing. First, the maximal notion of validity must be replaced by a new universal notion. Second, state-descriptions must make space for possible worlds understood as indices or points of evaluation. Last, a relation of accessibility between worlds needs to be introduced. Though Kripke is by no means the only logician in the fifties and early sixties to work on these ideas, it is in Kripke’s version of PWS that all these innovations are present. Kanger (1957), Montague (1960, but originally presented in 1955), Hintikka (1961), and Prior (1957) were all thinking of a relation between worlds, and Hintikka (1961) like Kripke (1959a) adopted a new notion of validity that required truth in all arbitrary sets of worlds. But Kripke was the only one to characterize the worlds as simple points of evaluation (in 1963a). Other logicians were still thinking of the worlds fundamentally as models of first-order logic, though perhaps Prior in his development of temporal logic was also moving towards a more abstract characterization of instants of time. Kripke’s more abstract characterization of the worlds is crucial in the provision of a link between the model theoretic semantics and the algebra of modal logic. Kripke saw very clearly this connection between the algebra and the semantics, and this made it possible for him to obtain model theoretic completeness and decidability results for various modal systems in a systematic way. Goldblatt (2003: section 4.8) argues convincingly that Kripke’s adoption of points of evaluation in the model structures is a particularly crucial innovation. Such a generalization opens the door to different future developments of the model theory and makes it possible to provide model theories for intensional logics in general. For these reasons, in this entry we devote more attention to Kripke’s version of PWS. For a more comprehensive treatment of the initial development of PWS, including the late fifties work on S5 of the French logician Bayart, the reader is referred to Goldblatt 2003. On the differences between Kanger’s semantics and standard PWS semantics, see Lindström 1996 and 1998.