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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. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, 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. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    4. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    5. Grant, Simon & Quiggin, John, "undated". "Learning and Discovery," Risk and Sustainable Management Group Working Papers 151174, University of Queensland, School of Economics.
    6. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
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