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/
Fellin, Giulio ;
Negri, Sara ;
Orlandelli, Eugenio
Constructive Cut Elimination in Geometric Logic
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: |
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Geometric theories, sequent calculi, axioms-as-rules, infinitary logic, constructive cut elimination |
Collection: |
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27th International Conference on Types for Proofs and Programs (TYPES 2021) |
Issue Date: |
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2022 |
Date of publication: |
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04.08.2022 |