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arXiv · 1610.02675

On the Mints Hierarchy in First-Order Intuitionistic Logic

Aleksy Schubert·Paweł Urzyczyn·Konrad Zdanowski
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Abstract

We stratify intuitionistic first-order logic over $(\forall,\to)$ into fragments determined by the alternation of positive and negative occurrences of quantifiers (Mints hierarchy). We study the decidability and complexity of these fragments. We prove that even the $\Delta_2$ level is undecidable and that $\Sigma_1$ is Expspace-complete. We also prove that the arity-bounded fragment of $\Sigma_1$ is complete for co-Nexptime.

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Aleksy Schubert, Paweł Urzyczyn, Konrad Zdanowski. 2016-10-09. On the Mints Hierarchy in First-Order Intuitionistic Logic. https://doi.org/10.2168/lmcs-12(4:11)2016

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