The Coinductive Formulation of Common Knowledge

  • Colm Baston
  • Venanzio CaprettaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10895)


We study the coinductive formulation of common knowledge in type theory. We formalise both the traditional relational semantics and an operator semantics, similar in form to the epistemic system S5, but at the level of events on possible worlds rather than as a logical derivation system. We have two major new results. Firstly, the operator semantics is equivalent to the relational semantics: we discovered that this requires a new hypothesis of semantic entailment on operators, not known in previous literature. Secondly, the coinductive version of common knowledge is equivalent to the traditional transitive closure on the relational interpretation. All results are formalised in the proof assistants Agda and Coq.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Functional Programming Lab, School of Computer ScienceUniversity of NottinghamNottinghamUK

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