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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 Proof-Theoretic Semantics for Exclusion.Nissim Francez & Michael Kaminski - 2017 - Logica Universalis 11 (4):489-505.
    The paper provides a proof-theory for a negative presentation of classical logic based on a single primitive of exclusion, generalizing the known presentation via the binary ‘nand. The completeness is established via deductive equivalence to Gentzens NK/LK systems.
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