A Completeness Theorem in Modal Logic
Kripke (Saul)
Source: Journal of Philosophical Logic 24.1, March 1959, pp. 1-14
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Philosophers Index Abstract

    A model theoretic semantics is given for quantified s5 with identity (with a fixed domain of individuals), based on the intuitive idea that necessity is truth in all "possible worlds." A completeness theorem is stated and proved, and tableau proof procedures and simple decision procedures for propositional s5 are given. It is stated that the methods will be extended to other modal1 systems in future publications.

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