Kripke, Saul (1940–)

Kripke, Saul(1940–)

Saul Kripke is an American logician and philosopher born in New York in 1940. After earning a BA from Harvard University in 1962, he held positions at Harvard, Rockefeller, Princeton, New York Universities, and elsewhere.

Modal Logic

Saul Kripke has worked in many branches of logic (higher recursion theory, set theory, models of arithmetic, and relevance logic), but the work best known to philosophers, and much cited in the literature of linguistic semantics, computer science, and other disciplines, is his development of Kripke models for modal and related logics. At the level of sentential logic such a model consists of a set X (of "states of the world," often misleadingly called "worlds"), a binary relation R (of "relative possibility") thereon, plus an assignment to each atomic formula p of the set of those x in X at which p is true. The assignment extends to all formulas, taking "Necessarily A" to be true at x if A is true at every y with xRy.

Kripke was the first to publish proofs of completeness theorems to the effect that truth at all x in all models with R reflexive (and transitive) (and symmetric) coincides with provability in the modal logic T (respectively S4) (respectively S5), and he obtained similar results for other modal logics.

Kripke, Saul (1940–) article

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