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

Anupam Das, Damien Pous, Michael Wagner
2018 Annual Conference for Computer Science Logic  
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.
doi:10.4230/lipics.csl.2018.19 dblp:conf/csl/DasP18 fatcat:5hg67ddwr5hu7fkiuryt4rl4ru