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Polish Logic 1920-1939

Philosophical Review 78 (4):539 (1969)

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  1. Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective).Richard Zach - 2015 - Journal of Philosophical Logic 45 (2):183-197.
    Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...)
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  • A system of ontology based on identity and partial ordering as an adequate logical apparatus for describing taxonomical structures of concepts.Toshiharu Waragai & Keiichi Oyamada - 2007 - Annals of the Japan Association for Philosophy of Science 15 (2):123-149.
  • Dual Equivalent Two-valued Under-determined and Over-determined Interpretations for Łukasiewicz’s 3-valued Logic Ł3.Gemma Robles, Francisco Salto & José M. Méndez - 2014 - Journal of Philosophical Logic 43 (2-3):303-332.
    Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley and Meyer’s basic positive (...)
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