Editing Kripke semantics (section)

==History and terminology==
{{Unreferenced section|date=October 2009}}
Similar work that predated Kripke's revolutionary semantic breakthroughs:{{sfn|Stokhof|2008|loc=See the last two paragraphs in Section 3 '''Quasi-historical Interlude: the Road from Vienna to Los Angeles'''.}}
* [[Rudolf Carnap]] seems to have been the first to have the idea that one can give a '''possible world semantics''' for the modalities of necessity and possibility by means of giving the valuation function a parameter that ranges over Leibnizian possible worlds.  Bayart develops this idea further, but neither gave recursive definitions of satisfaction in the style introduced by Tarski;
* J.C.C. McKinsey and [[Alfred Tarski]] developed an approach to modeling modal logics that is still influential in modern research, namely the algebraic approach, in which Boolean algebras with operators are used as models. [[Bjarni Jónsson]] and Tarski established the representability of Boolean algebras with operators in terms of frames. If the two ideas had been put together, the result would have been precisely frame models, which is to say Kripke models, years before Kripke. But no one (not even Tarski) saw the connection at the time.
*[[Arthur Prior]], building on unpublished work of [[C. A. Meredith]], developed a translation of sentential modal logic into classical predicate logic that, if he had combined it with the usual model theory for the latter, would have produced a model theory equivalent to Kripke models for the former. But his approach was resolutely syntactic and anti-model-theoretic.
* [[Stig Kanger]] gave a rather more complex approach to the interpretation of modal logic, but one that contains many of the key ideas of Kripke's approach.  He first noted the relationship between conditions on accessibility relations and [[C.I. Lewis|Lewis]]-style axioms for modal logic.  Kanger failed, however, to give a completeness proof for his system;
* [[Jaakko Hintikka]] gave a semantics in his papers introducing epistemic logic that is a simple variation of Kripke's semantics, equivalent to the characterisation of valuations by means of maximal consistent sets.  He doesn't give inference rules for epistemic logic, and so cannot give a completeness proof;
* [[Richard Montague]] had many of the key ideas contained in Kripke's work, but he did not regard them as significant, because he had no completeness proof, and so did not publish until after Kripke's papers had created a sensation in the logic community;
* [[Evert Willem Beth]] presented a semantics of intuitionistic logic based on trees, which closely resembles Kripke semantics, except for using a more cumbersome definition of satisfaction.