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Reasoning about knowledge of unawareness

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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.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 67 (2009)
Issue (Month): 2 (November)
Pages: 503-525

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Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:503-525

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Modal logic Awareness Axiomatization Decidability Multi-agent system Interactive epistemology;

References

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  1. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, 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., 2004. "Interactive unawareness," CORE Discussion Papers 2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Grant, Simon & Quiggin, John, 2006. "Learning and Discovery," Risk and Sustainable Management Group Working Papers 151174, University of Queensland, School of Economics.
  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. 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, December.
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Citations

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Cited by:
  1. Halpern, Joseph Y. & Rêgo, Leandro C., 2013. "Reasoning about knowledge of unawareness revisited," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 73-84.
  2. Feinberg, Yossi, 2012. "Games with Unawareness," Research Papers 2122, Stanford University, Graduate School of Business.
  3. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
  4. Grant, Simon & Quiggin, John, 2012. "Inductive Reasoning About Unwareness," Risk and Sustainable Management Group Working Papers 151202, University of Queensland, School of Economics.
  5. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
  6. Tsakas Elias, 2012. "Rational belief hierarchies," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  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. Grant, Simon & Quiggin, John, 2012. "Bounded Awareness, Heuristics and the Precautionary Principle," Risk and Sustainable Management Group Working Papers 151203, University of Queensland, School of Economics.
  9. 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.

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