Journal of Philosophical Logic

, Volume 45, Issue 2, pp 183–197 | Cite as

Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective)

  • Richard ZachEmail author


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.


Natural deduction Sequent calculus Sheffer stroke 



I am grateful to Allen Hazen and Jeff Pelletier for helpful comments as well as the question which originally prompted this paper.


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of CalgaryCalgaryCanada

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