2-Sequent calculus: a proof theory of modalities

Abstract

Masini, A., 2-Sequent calculus: a proof theory of modalities, Annals of Pure and Applied Logic 58 (1992) 229–246. In this work we propose an extension of the Getzen sequent calculus in order to deal with modalities. We extend the notion of a sequent obtaining what we call a 2-sequent. For the obtained calculus we prove a cut elimination theorem.