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Mathematics of Public Announcements

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Logic, Rationality, and Interaction (LORI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6953))

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Abstract

We study some mathematical aspects of public announcement logic (PAL) and its several variants. By a model-theoretic approach, we explore van Benthem’s result that uses recursion axioms to characterize the submodel operation, and show some model-theoretic results on the respecting phenomena. The second approach to understand public announcements is algebraic. Based on a joint work with A. Palmigiano and M. Sadrzadeh, we treat public announcements as devices for getting a new quotient algebra updated by an element in the original one. Then we show the algebraic soundness and completeness result for PAL and generalize this approach to PAL extension of epistemic intuitionistic modal logic. Finally, we give some observations on the PAL extensions of first-order logic as well as epistemic predicate modal logic.

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Author information

Authors and Affiliations

  1. Institute of Logic and Intelligence, Southwest University, Beibei, Chongqing, China, 400715

    Minghui Ma

Authors
  1. Minghui Ma
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Editor information

Editors and Affiliations

  1. University of Sevilla, Camilo José Cela s/n, 41018, Sevilla, Spain

    Hans van Ditmarsch

  2. Université Paul Sabatier, IRIT, 118 Route de Narbonne, 31062, Toulouse Cedex 04, France

    Jérôme Lang

  3. Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, 510275, Guangzhou, China

    Shier Ju

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© 2011 Springer-Verlag Berlin Heidelberg

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Ma, M. (2011). Mathematics of Public Announcements. In: van Ditmarsch, H., Lang, J., Ju, S. (eds) Logic, Rationality, and Interaction. LORI 2011. Lecture Notes in Computer Science(), vol 6953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24130-7_14

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  • DOI: https://doi.org/10.1007/978-3-642-24130-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24129-1

  • Online ISBN: 978-3-642-24130-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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