Natural Deduction for the Sheffer Stroke and Peirce's Arrow (And Any Other Truth-Functional Connective)
Logic
2017-10-27 v2
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.
Keywords
Cite
@article{arxiv.1504.05995,
title = {Natural Deduction for the Sheffer Stroke and Peirce's Arrow (And Any Other Truth-Functional Connective)},
author = {Richard Zach},
journal= {arXiv preprint arXiv:1504.05995},
year = {2017}
}