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The Stroke Function in Natural Deduction

Robert Price

Mathematical Logic Quarterly 7 (7-10):117-123 (1961)

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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.details 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 (...) the connectives in question. (shrink) Download Export citation Bookmark 3 citations
Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different.Allen P. Hazen & Francis Jeffry Pelletier - 2014 - Studia Logica 102 (6):1103-1142.details Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...) Download Export citation Bookmark 10 citations
Dung’s Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce–Quine Dagger.Dov M. Gabbay - 2011 - Logica Universalis 5 (2):255-318.details In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce–Quine dagger connective of classical logic which can generate the other connectives ${\neg, \wedge, \vee, \to}$ of classical logic. After establishing the above correspondence we offer variations of the Dung argumentation frames in parallel to variations of classical logic, such as resource logics, predicate logic, etc., etc., and create resource argumentation (...) Download Export citation Bookmark 5 citations
A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.details Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...) Download Export citation Bookmark 35 citations
Minimal Complete Propositional Natural Deduction Systems.Amr Elnashar & Wafik Boulos Lotfallah - 2018 - Journal of Philosophical Logic 47 (5):803-815.details For each truth-functionally complete set of connectives, we construct a sound and complete natural deduction system containing no axioms and the smallest possible number of inference rules, namely one. Download Export citation Bookmark

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