Non-wellfounded proof theory for (Kleene+action)(algebras+lattices)

Anupam Das (1) , Damien Pous (2)

1 ITU - IT University of Copenhagen
2 LIP - Laboratoire de l'Informatique du Parallélisme

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.

Mots clés: Kleene algebra; proof theory; sequent system; non-wellfounded proofs; action algebra; action lattices

Domaines: Logique en informatique [cs.LO]

Anupam Das, Damien Pous. Non-wellfounded proof theory for (Kleene+action)(algebras+lattices). 2018. ⟨hal-01703942v2⟩