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DOI: 10.4230/LIPIcs.CSL.2023.9

Proofs and Refutations for Intuitionistic and Second-Order Logic

Authors: Pablo Barenbaum and Teodoro Freund

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract

The λ^{PRK}-calculus is a typed λ-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend λ^{PRK} to encompass classical second-order logic, by incorporating parametric polymorphism and existential types. The system is shown to enjoy good computational properties, such as type preservation, confluence, and strong normalization, which is established by means of a reducibility argument. We identify a syntactic restriction on proofs that characterizes exactly the intuitionistic fragment of second-order λ^{PRK}, and we study canonicity results.

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Pablo Barenbaum and Teodoro Freund. Proofs and Refutations for Intuitionistic and Second-Order Logic. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{barenbaum_et_al:LIPIcs.CSL.2023.9,
  author =	{Barenbaum, Pablo and Freund, Teodoro},
  title =	{{Proofs and Refutations for Intuitionistic and Second-Order Logic}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.9},
  URN =		{urn:nbn:de:0030-drops-174707},
  doi =		{10.4230/LIPIcs.CSL.2023.9},
  annote =	{Keywords: lambda-calculus, propositions-as-types, classical logic, proof normalization}
}

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Proofs and Refutations for Intuitionistic and Second-Order Logic

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