Cut elimination by unthreading

Abstract

Abstract We provide a non-Gentzen, though fully syntactical, cut-elimination algorithm for classical propositional logic. The designed procedure is implemented on $$\textsf{GS4}$$ GS 4 , the one-sided version of Kleene’s sequent system $$\textsf{G4}$$ G 4 . 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 $$\textsf{GS4}$$ GS 4 -proofs.