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Kripke, Saul A.
A Completeness Theorem in Modal Logic" WITH Abstracts of "Distinguished Constituents", "Semantical Analysis of Modal Logic", "The Problem of Entailment" in The Journal of Symbolic Logic Vol. 24, Issue No. 1, March 1959 pp. 1-14 WITH Vol. 24, Issue No. 4, Dec. 1959 pp. 323-324
Princeton: Association for Symbolic Logic, 1959. FIRST EDITION, FIRST IMPRESSION IN PRISTINE ORIGINAL WRAPS OF SAUL KRIPKE'S SEMINAL FIRST PAPER ON MODAL LOGIC, "A Completeness Theorem in Modal Logic". The paper presents Kripke's important ideas on the semantics of modal logic, or the logic of modal notions like necessity and possibility. Included are all 4 Journal issues for 1959, one of which is inclusive of abstracts of 3 other papers Kripke sent to the Journal. "Universally hailed" for this work, in this paper, Kripke both proves the formal completeness of modal logic (supplemented by first-order quantifiers and the sign of equality) and "create[s] a semantics, now called Kripke semantics" (Hurley, Logic: The Essentials, 217). Kripke semantics "is a formals semantics for non-classical logic systems... first conceived for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The discovery of Kripke semantics was a breakthrough in the theory of non-classical logics, because the model theory of such logics was almost non-existent before Kripke (algebraic semantics existed, but were considered 'syntax in disguise'). (Wikipedia). Saul Kripke grew up in Omaha, Nebraska, and in 1959, he mailed this paper to The Journal of Symbolic Logic. As the story goes, the Kripke wrote his completeness theorem in modal logic at age 17; the paper was sent out for comments, to, among a number of others, the head of the Harvard mathematics department. This person then wrote Kripke urging him to apply for a job at Harvard. The reply he received read: "My … [Click Below for Full Description]
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