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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: 2018


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