Francesca Poggiolesi

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.

In this paper we present a sequent calculus for the multi-agent system S5 m . First, we introduce a particularly simple alternative Kripke semantics for the system S5 m . Then, we construct a hypersequent calculus for S5 m that reflects at the syntactic level this alternative interpretation. We prove that this hypersequent calculus is theoremwise equivalent to the Hilbert-style system S5 m , that it is contraction-free and cut-free, and finally that it is decidable. All results are proved in a purely syntactic way and the cut-elimination procedure yields an upper bound of ip 2 (n, 0) where ip 2 is an hyperexponential function of base 2.