Cut-Elimination for the Modal Grzegorczyk Logic via Non-well-founded Proofs

Abstract

Abstract. We present a sequent calculus for the modal Grzegorczyk logic Grz allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.

Cut Elimination for the Weak Modal Grzegorczyk Logic via Non-well-Founded Proofs

“…Recently a new proof-theoretic presentation for the logic GL in the form of a sequent calculus allowing non-well-founded proofs was given in [10,4]. Later, the same ideas were applied to the modal Grzegorczyk logic Grz in [8,7], where it allowed to prove several proof-theoretic properties of this logic syntactically.…”

Non-Well-Founded Proofs for the Grzegorczyk Modal Logic

“…Here we present a sequent calculus for the Grzegorczyk modal logic allowing non-well-founded proofs and obtain the cut-elimination theorem for it. This article is an extended version of the conference paper [15].…”