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Natural Deduction for the Sheffer Stroke and Peirce's Arrow (And Any Other Truth-Functional Connective)

Source

Richard Zach, "Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective)," Journal of Philosophical Logic, (2015), forthcoming.

Abstract

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 (NAND) and Peirce's arrow (NOR). 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.

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doi: 10.1007/s10992-015-9370-x

Free Preprint from arXiv

arxiv.org/abs/1504.05995