• Corpus ID: 208527265

# Negative Translations for Affine and Lukasiewicz Logic

@article{Arthan2019NegativeTF,
title={Negative Translations for Affine and Lukasiewicz Logic},
author={Rob Arthan and Paulo Oliva},
journal={ArXiv},
year={2019},
volume={abs/1912.00012}
}
• Published 29 November 2019
• Mathematics, Computer Science
• ArXiv
We investigate four well-known negative translations of classical logic into intuitionistic logic within a substructural setting. We find that in affine logic the translation schemes due to Kolmogorov and Godel both satisfy Troelstra's criteria for a negative translation. On the other hand, the schemes of Glivenko and Gentzen both fail for affine logic, but for different reasons: one can extend affine logic to make Glivenko work and Gentzen fail and vice versa. By contrast, in the setting of…
1 Citations

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