On the importance of being analytic. The paradigmatic case of the logic of proofs

Abstract

International audience In the recent literature on proof theory, there seems to be a new raising topic which consists in identifying those properties that characterise a good sequent calculus. The property that has received by far the most attention is the analyticity property. In this paper we propose a new argument in support of the analyticity property. We will do it by means of the example of the logic of proofs, a logic recently introduced by Artemov [1]. Indeed a detailed proof analysis of this logic sheds new light on the logic itself and perfectly exemplifies our argument in favour of the analiticity.