License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2021.7
URN: urn:nbn:de:0030-drops-167763
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16776/
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Fellin, Giulio ; Negri, Sara ; Orlandelli, Eugenio

Constructive Cut Elimination in Geometric Logic

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LIPIcs-TYPES-2021-7.pdf (0.8 MB)

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.

BibTeX - Entry

@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/opus/volltexte/2022/16776},
  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}
}

Keywords: Geometric theories, sequent calculi, axioms-as-rules, infinitary logic, constructive cut elimination
Collection: 27th International Conference on Types for Proofs and Programs (TYPES 2021)
Issue Date: 2022
Date of publication: 04.08.2022

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