Strong Normalisation of Cut-Elimination in Classical Logic

Abstract. In this paper a strongly normalising cut-elimination procedure is presented for classical logic. The procedure adapts the standard cut transformations, see for example [12]. In particular our cutelimination procedure requires no special annotations on formulae. We design a term calculus for a variant of Kleene’s sequent calculus G3 via the Curry-Howard correspondence and the cut-elimination steps are given as rewrite rules. In the strong normalisation proof we adapt the symmetric reducibility candidates developed by Barbanera and Berardi.