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Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model

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  • Gaia Belardinelli
  • Rasmus K. Rendsvig

Abstract

Heifetz, Meier and Schipper (HMS) present a lattice model of awareness. The HMS model is syntax-free, which precludes the simple option to rely on formal language to induce lattices, and represents uncertainty and unawareness with one entangled construct, making it difficult to assess the properties of either. Here, we present a model based on a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show the models to be equivalent by defining transformations between them which preserve formula satisfaction, and obtain completeness through our and HMS' results.

Suggested Citation

  • Gaia Belardinelli & Rasmus K. Rendsvig, 2020. "Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model," Papers 2012.12982, arXiv.org.
    • Handle: RePEc:arx:papers:2012.12982
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    References listed on IDEAS

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    1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2008. "A canonical model for interactive unawareness," Games and Economic Behavior, Elsevier, vol. 62(1), pages 304-324, January.
    2. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
    3. Halpern, Joseph Y. & Rêgo, Leandro C., 2013. "Reasoning about knowledge of unawareness revisited," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 73-84.
    4. Brian Hill, 2010. "Awareness Dynamics," Post-Print hal-00521801, HAL.
    5. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    6. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    7. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.
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