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DOI: 10.4230/LIPIcs.CSL.2018.19
URN: urn:nbn:de:0030-drops-96869
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9686/
Das, Anupam ; Pous, Damien
Non-Wellfounded Proof Theory For (Kleene+Action)(Algebras+Lattices)
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Abstract
We prove cut-elimination for a sequent-style proof system which is sound and complete for the equational theory of Kleene algebra, and where proofs are (potentially) non-wellfounded infinite trees. We extend these results to systems with meets and residuals, capturing `star-continuous' action lattices in a similar way. We recover the equational theory of all action lattices by restricting to regular proofs (with cut) - those proofs that are unfoldings of finite graphs.
BibTeX - Entry
@InProceedings{das_et_al:LIPIcs:2018:9686,
author = {Anupam Das and Damien Pous},
title = {{Non-Wellfounded Proof Theory For (Kleene+Action)(Algebras+Lattices)}},
booktitle = {27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
pages = {19:1--19:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-088-0},
ISSN = {1868-8969},
year = {2018},
volume = {119},
editor = {Dan Ghica and Achim Jung},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9686},
URN = {urn:nbn:de:0030-drops-96869},
doi = {10.4230/LIPIcs.CSL.2018.19},
annote = {Keywords: Kleene algebra, proof theory, sequent system, non-wellfounded proofs}
}
| Keywords: | Kleene algebra, proof theory, sequent system, non-wellfounded proofs | |
| Seminar: | 27th EACSL Annual Conference on Computer Science Logic (CSL 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 29.08.2018 |
