Common knowledge: a finitary calculus with a syntactic cut-elimination procedure


Logique et Analyse

June 2015, vol. 58, n°230, pp. 279-306

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

In this paper we present a finitary sequent calculus for the S5 multi-modal system with common knowledge. The sequent calculus is based on indexed hyper-sequents which are standard hypersequents refined with indices that serve to show the multi-agent feature of the system S5. The calculus has a non-analytic right introduction rule. We prove that the calculus is contraction- and weakening-free, that (almost all) its logical rules are invertible, and finally that it enjoys a syntactic cut-elimination procedure. Moreover, the use of the non-analytic rule can be restricted so that the calculus can be considered as suitable for proof search