Non-Wellfounded Proof Theory For (Kleene+Action)(Algebras+Lattices)

Authors Anupam Das, Damien Pous

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Anupam Das
  • University of Copenhagen, Copenhagen, Denmark
Damien Pous
  • Univ Lyon, CNRS, ENS de Lyon, UCB Lyon 1, LIP, Lyon, France

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Anupam Das and Damien Pous. Non-Wellfounded Proof Theory For (Kleene+Action)(Algebras+Lattices). In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
  • Theory of computation → Regular languages
  • Kleene algebra
  • proof theory
  • sequent system
  • non-wellfounded proofs


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