There is a simple technique, due to Dragalin, for proving strong cut-elimination for intuitionistic sequent calculus, but the technique is constrained to certain choices of reduction rules, preventing equally natural alternatives. We consider such a natural, alternative set of reduction rules and show that the classical technique is inapplicable. Instead we develop another approach combining two of our favorite tools—Klop’s ι-translation and perpetual reductions. These tools are of independent interest and have proved useful in a variety of settings; it is therefore natural to investigate, as we do here, what they have to offer the field of sequent calculus.
"Strong cut-elimination in sequent calculus using Klop’s ι-translation and perpetual reductions." J. Symbolic Logic 73 (3) 919 - 932, September 2008. https://doi.org/10.2178/jsl/1230396755