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Reasoning about knowledge of unawareness revisited

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  • Halpern, Joseph Y.
  • Rêgo, Leandro C.

Abstract

In earlier work (Halpern and Rêgo, 2009), we proposed a logic that extends the Logic of General Awareness of Fagin and Halpern (1988) by allowing quantification over primitive propositions. This makes it possible to express the fact that an agent knows that there are some facts of which he is unaware. In that logic, it is not possible to model an agent who is uncertain about whether he is aware of all formulas. To overcome this problem, we keep the syntax of the earlier paper, but allow models where, with each world, a possibly different language is associated. We provide a sound and complete axiomatization for this logic and show that, under natural assumptions, the quantifier-free fragment of the logic is characterized by exactly the same axioms as the logic of Heifetz et al. (2008).

Suggested Citation

  • Halpern, Joseph Y. & Rêgo, Leandro C., 2013. "Reasoning about knowledge of unawareness revisited," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 73-84.
    • Handle: RePEc:eee:matsoc:v:65:y:2013:i:2:p:73-84
    DOI: 10.1016/j.mathsocsci.2012.08.003
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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. Oliver Walker, 2011. "Unawareness with �possible� possible worlds," GRI Working Papers 69, Grantham Research Institute on Climate Change and the Environment.
    3. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
    4. Oliver Board, 2008. "Object-Based Unawareness: Theory and Applications," Working Paper 378, Department of Economics, University of Pittsburgh, revised Mar 2009.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    6. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    7. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    8. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, April.
    9. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
    10. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    11. 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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    Citations

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    Cited by:

    1. Wenjun Ma & Burkhard C. Schipper, 2017. "Does exposure to unawareness affect risk preferences? A preliminary result," Theory and Decision, Springer, vol. 83(2), pages 245-257, August.
    2. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 145, University of California, Davis, Department of Economics.
    3. Piermont, Evan, 2017. "Introspective unawareness and observable choice," Games and Economic Behavior, Elsevier, vol. 106(C), pages 134-152.
    4. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org.
    5. Karni, Edi & Vierø, Marie-Louise, 2017. "Awareness of unawareness: A theory of decision making in the face of ignorance," Journal of Economic Theory, Elsevier, vol. 168(C), pages 301-328.
    6. Gaia Belardinelli & Rasmus K. Rendsvig, 2021. "Awareness Logic: Kripke Lattices as a Middle Ground between Syntactic and Semantic Models," Papers 2106.12868, arXiv.org.
    7. Evan Piermont, 2023. "Iterated Revelation: How to Incentive Experts to Complete Incomplete Contracts," Papers 2304.05142, arXiv.org, revised Mar 2024.
    8. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 153, University of California, Davis, Department of Economics.
    9. Yoshihiko Tada, 2024. "AU Introspection and Symmetry under non-trivial unawareness," Theory and Decision, Springer, vol. 97(2), pages 409-421, September.
    10. Marie-Louise Vierø, 2022. "Lost in objective translation: Awareness of unawareness when unknowns are not simply unknowns," Economics Working Papers 2022-06, Department of Economics and Business Economics, Aarhus University.
    11. Joseph Y. Halpern & Evan Piermont, 2020. "Dynamic Awareness," Papers 2007.02823, arXiv.org.
    12. Gaia Belardinelli & Rasmus K. Rendsvig, 2020. "Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model," Papers 2012.12982, arXiv.org.
    13. Wenjun Ma & Burkhard C. Schipper, 2017. "Does exposure to unawareness affect risk preferences? A preliminary result," Theory and Decision, Springer, vol. 83(2), pages 245-257, August.
    14. Patrick H. O'Callaghan, 2019. "Second-order Inductive Inference: an axiomatic approach," Papers 1904.02934, arXiv.org, revised Mar 2021.

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