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Pairing Traditional and Generic Common Knowledge

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Logical Foundations of Computer Science (LFCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9537))

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Abstract

Common Knowledge C is a standard tool in epistemic logics. Generic Common Knowledge J is an alternative which has desirable logical behavior such as cut-elmination and which can be used in place of C in the analysis of many games and epistemic senarios. In order to compare their deductive strengths directly we define the multi-agent logic \(\mathsf{S4}_n^{CJ}\) built on a language with both C and J operators in addition to agents’ \(K_i\)s so that any finite prefix of modal operators is acceptable. We prove \(\mathsf{S4}_n^{CJ}\) is complete, decidable, and that \(J\varphi \rightarrow C\varphi \) though not \(C\varphi \rightarrow J\varphi \). Additional epistemic scenarios may be investigated which take advantage of this dual layer of common knowledge agents.

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Authors and Affiliations

  1. Bronx Community College, CUNY, Bronx, NY, USA

    Evangelia Antonakos

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  1. Evangelia Antonakos
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Correspondence to Evangelia Antonakos .

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Editors and Affiliations

  1. City University of New York , New York, New York, USA

    Sergei Artemov

  2. Cornell University , Ithaca, New York, USA

    Anil Nerode

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© 2016 Springer International Publishing Switzerland

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Antonakos, E. (2016). Pairing Traditional and Generic Common Knowledge. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2016. Lecture Notes in Computer Science(), vol 9537. Springer, Cham. https://doi.org/10.1007/978-3-319-27683-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-27683-0_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27682-3

  • Online ISBN: 978-3-319-27683-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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