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Reasoning about knowledge of unawareness

Author

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

Abstract

Awareness has been shown to be a useful addition to standard epistemic logic. However, standard propositional logics for knowledge and awareness cannot express the fact that an agent knows that there are facts of which he is unaware without there being an explicit fact that the agent knows he is unaware of. We extend Fagin and Halpern's logic of general awareness to a logic that allows quantification over variables, so that there is a formula in the language that says "an agent explicitly knows that there exists a fact of which he is unaware." Moreover, that formula can be true without the agent explicitly knowing that he is unaware of any particular formula. We provide a sound and complete axiomatization of the logic. Finally, we show that the validity problem for the logic is recursively enumerable, but not decidable.

Suggested Citation

  • Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.
  • Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:503-525
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    References listed on IDEAS

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    1. 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, January.
    2. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    3. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    4. Simon Grant & John Quiggin, 2005. "Learning and Discovery," Risk & Uncertainty Working Papers WP7R05, Risk and Sustainable Management Group, University of Queensland.
    5. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    6. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
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    Citations

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    Cited by:

    1. repec:kap:theord:v:83:y:2017:i:2:d:10.1007_s11238-017-9594-z is not listed on IDEAS
    2. Heinsalu, Sander, 2012. "Equivalence of the information structure with unawareness to the logic of awareness," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2453-2468.
    3. Simon Grant & John Quiggin, 2015. "A preference model for choice subject to surprise," Theory and Decision, Springer, vol. 79(2), pages 167-180, September.
    4. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    5. Friederike Mengel & Elias Tsakas & Alexander Vostroknutov, 2016. "Past experience of uncertainty affects risk aversion," Experimental Economics, Springer;Economic Science Association, vol. 19(1), pages 151-176, March.
    6. 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.
    7. 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.
    8. Simon Grant & John Quiggin, 2013. "Inductive reasoning about unawareness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 717-755, November.
    9. Feinberg, Yossi, 2012. "Games with Unawareness," Research Papers 2122, Stanford University, Graduate School of Business.
    10. Halpern, Joseph Y. & Rêgo, Leandro C., 2013. "Reasoning about knowledge of unawareness revisited," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 73-84.
    11. Tsakas Elias, 2012. "Rational belief hierarchies," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. repec:eee:gamebe:v:106:y:2017:i:c:p:134-152 is not listed on IDEAS
    13. Grant, Simon & Quiggin, John, 2013. "Bounded awareness, heuristics and the Precautionary Principle," Journal of Economic Behavior & Organization, Elsevier, vol. 93(C), pages 17-31.
    14. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
    15. 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.

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