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The Coinductive Formulation of Common Knowledge

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Interactive Theorem Proving (ITP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10895))

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Abstract

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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Notes

  1. 1.

    https://colmbaston.co.uk/files/Common-Knowledge.agda.

  2. 2.

    http://www.duplavis.com/venanzio/publications/common_knowledge.v.

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Authors and Affiliations

  1. Functional Programming Lab, School of Computer Science, University of Nottingham, Nottingham, UK

    Colm Baston & Venanzio Capretta

Authors
  1. Colm Baston
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  2. Venanzio Capretta
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Correspondence to Venanzio Capretta .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    Jeremy Avigad

  2. Inria, Nantes, France

    Assia Mahboubi

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Baston, C., Capretta, V. (2018). The Coinductive Formulation of Common Knowledge. In: Avigad, J., Mahboubi, A. (eds) Interactive Theorem Proving. ITP 2018. Lecture Notes in Computer Science(), vol 10895. Springer, Cham. https://doi.org/10.1007/978-3-319-94821-8_8

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  • DOI: https://doi.org/10.1007/978-3-319-94821-8_8

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  • Online ISBN: 978-3-319-94821-8

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