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The Ryōan-ji axiom for common knowledge on hypergraphs

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Abstract

The article studies common knowledge in communication networks with a fixed topological structure. It introduces a non-trivial principle, called the Ryōan-ji axiom, which captures logical properties of common knowledge of all protocols with a given network topology. A logical system, consisting of the Ryōan-ji axiom and two additional axioms, is proven to be sound and complete.

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Notes

  1. Otherwise, two operatives of agency \(C\) on different islands could easily form common knowledge amongst \(A\), \(B\), and \(C\).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, McDaniel College, Westminster, MD, 21157, USA

    Jeffrey Kane & Pavel Naumov

Authors
  1. Jeffrey Kane
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  2. Pavel Naumov
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Correspondence to Pavel Naumov.

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Kane, J., Naumov, P. The Ryōan-ji axiom for common knowledge on hypergraphs. Synthese 191, 3407–3426 (2014). https://doi.org/10.1007/s11229-014-0455-9

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  • DOI: https://doi.org/10.1007/s11229-014-0455-9

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