The Proof Theory of Common Knowledge

  • Michel Marti
  • Thomas Studer
Part of the Outstanding Contributions to Logic book series (OCTR, volume 12)


Common knowledge of a proposition A can be characterized by the following infinitary conjunction: everybody knows A and everybody knows that everybody knows A and everybody knows that everybody knows that everybody knows A and so on. We present a survey of deductive systems for the logic of common knowledge. In particular, we present two different Hilbert-style axiomatizations and two infinitary cut-free sequent systems. Further we discuss the problem of syntactic cut-elimination for common knowledge. The paper concludes with a list of open problems.


Common knowledge Multi-agent systems Proof theory Infinitary deductive systems Cut-elimination 



We would like to thank Rajeev Goré for many helpful comments. This research is supported by the SNSF project 153169.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.University of BernBernSwitzerland

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