Full Cut-Elimination for Stratified or Total Definitions

Prove full cut-elimination for the cyclic sequent calculus for non-monotone inductive definitions on sequents with stratified definitions, or, more broadly, on sequents with total definitions.

Background

The paper establishes a cut-restriction theorem for stratified definitions: every provable sequent can be proved using only elementary cuts of a specified form. Full cut-elimination is proved for the infinitary calculus on positive definitions but not for the cyclic calculus. The authors explicitly state that it is unresolved whether the cyclic cut-restriction result can be strengthened, possibly even for total definitions.