The Review of Symbolic Logic

Research Article

A PURELY SYNTACTIC AND CUT-FREE SEQUENT CALCULUS FOR THE MODAL LOGIC OF PROVABILITY

FRANCESCA POGGIOLESIa1 c1

a1 Centre For Logic and Philosophy of Science, Vrije Universiteit Brussel

Abstract

In this paper we present a sequent calculus for the modal propositional logic GL (the logic of provability) obtained by means of the tree-hypersequent method, a method in which the metalinguistic strength of hypersequents is improved, so that we can simulate trees shapes. We prove that this sequent calculus is sound and complete with respect to the Hilbert-style system GL, that it is contraction free and cut free and that its logical and modal rules are invertible. No explicit semantic element is used in the sequent calculus and all the results are proved in a purely syntactic way.

(Received May 29 2008)

Correspondence:

c1 CENTRE FOR LOGIC AND PHILOSOPHY OF SCIENCE, VRIJE UNIVERSITEIT BRUSSEL, ETTERBEEK CAMPUS, PLEINLAAN 2, B-1050 BRUSSELS, BELGIUM E-mail: poggiolesi@gmail.com