Cut elimination by unthreading

Abstract

We provide a non-Gentzen, though fully syntactical, cut-elimination algorithm for classical propositional logic. The designed procedure is implemented on \(\textsf{GS4}\), the one-sided version of Kleene’s sequent system \(\textsf{G4}\). The algorithm here proposed proves to be more ‘dexterous’ than other, more traditional, Gentzen-style techniques as the size of proofs decreases at each step of reduction. As a corollary result, we show that analyticity always guarantees minimality of the size of \(\textsf{GS4}\)-proofs.