NON-WELL-FOUNDED PROOFS FOR THE GRZEGORCZYK MODAL LOGIC
Yury Savateev, Daniyar Salkarbekovich Shamkanov · The Review of Symbolic Logic · 2020
Abstract We present a sequent calculus for the Grzegorczyk modal logic $\mathsf {Grz}$ allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs. As an application, we establish the Lyndon interpolation property for the logic $\mathsf {Grz}$ proof-theoretically.