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Traditional logic

A. N. Prior

In Paul Edwards (ed.), The Encyclopedia of philosophy. New York,: Macmillan. pp. 5--34 (1967)

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Syllogistics = monotonicity + symmetry + existential import.Jan van Eijck - unknowndetails Syllogistics reduces to only two rules of inference: monotonicity and symmetry, plus a third if one wants to take existential import into account. We give an implementation that uses only the monotonicity and symmetry rules, with an addendum for the treatment of existential import. Soundness follows from the monotonicity properties and symmetry properties of the Aristotelean quantiﬁers, while completeness for syllogistic theory is proved by direct inspection of the valid syllogisms. Next, the valid syllogisms are decomposed in terms of the (...) Download Export citation Bookmark 2 citations
(2 other versions)First-order modal theories III — facts.Kit Fine - 1982 - Synthese 53 (1):43-122.details Download Export citation Bookmark 57 citations
Arthur N. Prior and the Lvov-Warsaw School.Zuzana Rybaříková - 2023 - History and Philosophy of Logic 44 (1):91-103.details This paper presents the link between Arthur N. Prior and logicians that belonged to the Lvov-Warsaw School. Although certain members of the Lvov-Warsaw School influenced Prior’s views, the amount and the form of the impact are still under discussion. Prior also cooperated with some of them in the development of his systems of logic. This paper focuses on four main areas in which Prior admitted adopting ideas from the Lvov-Warsaw School: systems of propositional logic, the history of logic, modal and (...) Download Export citation Bookmark 1 citation
(1 other version)Head or tail? de morgan on the bounds of traditional logic.Víctor Sánchez Valencia - 1997 - History and Philosophy of Logic 18 (3):123-138.details This paper is concerned with De Morgan’s explanation of the validity of arguments that involve relational notions. It discusses De Morgan’s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan’s logic, and contrary to that De Morgan’s mistake is not beyond repair. The rules that determine his new logic (...) Download Export citation Bookmark 1 citation
Natural logic for natural language.Jan van Eijck - manuscriptdetails We implement the extension of the logical consequence relation to a partial order ≤ on arbitary types built from e (entities) and t (Booleans) that was given in [1], and the definition of monotonicity preserving and monotonicity reversing functions in terms of ≤. Next, we present a new algorithm for polarity marking, and implement this for a particular fragment of syntax. Finally, we list the reseach agenda that these definitions and this algorithm suggest. The implementations use Haskell [8], and are (...) Download Export citation Bookmark 9 citations
Logic, Language, and Computation: 6th International Tbilisi Symposium on Logic, Language, and Computation, Tbillc 2005, Batumi, Georgia, September 12-16, 2005. Revised Selected Papers.Balder D. ten Cate (ed.) - 2007 - Berlin and Heidelberg: Springer.details Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book represents the thoroughly refereed post-proceedings of the 6th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2005, held in Batumi, Georgia. The 19 revised full papers presented were carefully reviewed and selected from numerous presentations at the symposium. The papers present current research in all aspects of linguistics, logic and computation. Download Export citation Bookmark

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