# 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} }

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… Expand

#### One Citation

A Curry-Howard Correspondence for the Minimal Fragment of Łukasiewicz Logic

- Computer Science, Mathematics
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A term calculus is introduced which adds to the affine $\lambda$-calculus with pairing a new construct allowing for a restricted form of contraction and it is proved that ${\cal B}$ is strongly normalising and has the Church-Rosser property. Expand

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