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DOI: 10.4230/LIPIcs.TYPES.2021.7

Constructive Cut Elimination in Geometric Logic

Authors: Giulio Fellin, Sara Negri, and Eugenio Orlandelli

Published in: LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021)

Abstract

A constructivisation of the cut-elimination proof for sequent calculi for classical and intuitionistic infinitary logic with geometric rules - given in earlier work by the second author - is presented. This is achieved through a procedure in which the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer’s Bar Induction. Additionally, a proof of Barr’s Theorem for geometric theories that uses only constructively acceptable proof-theoretical tools is obtained.

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Giulio Fellin, Sara Negri, and Eugenio Orlandelli. Constructive Cut Elimination in Geometric Logic. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fellin_et_al:LIPIcs.TYPES.2021.7,
  author =	{Fellin, Giulio and Negri, Sara and Orlandelli, Eugenio},
  title =	{{Constructive Cut Elimination in Geometric Logic}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.7},
  URN =		{urn:nbn:de:0030-drops-167763},
  doi =		{10.4230/LIPIcs.TYPES.2021.7},
  annote =	{Keywords: Geometric theories, sequent calculi, axioms-as-rules, infinitary logic, constructive cut elimination}
}

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Constructive Cut Elimination in Geometric Logic

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