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

Francesca Poggiolesi, Brian Hill


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. 


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