A Linear Perspective on Cut-Elimination for Non-wellfounded Sequent Calculi with Least and Greatest Fixed-Points

Abstract

AbstractThis paper establishes cut-elimination for $$\mathsf {\mu LL^\infty }$$, $$\mathsf {\mu LK^\infty }$$ and $$\mathsf {\mu LJ^\infty }$$, that are non-wellfounded sequent calculi with least and greatest fixed-points, by expanding on prior works by Santocanale and Fortier [20] as well as Baelde et al. [3, 4]. The paper studies a fixed-point encoding of $$\textsf{LL}$$ exponentials in order to deduce those cut-elimination results from that of $$\mathsf {\mu MALL^\infty }$$. Cut-elimination for $$\mathsf {\mu LK^\infty }$$ and $$\mathsf {\mu LJ^\infty }$$ is obtained by developing appropriate linear decorations for those logics.