Reasoning about knowledge of unawareness
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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, June.
- Grant, Simon & Quiggin, John, 2006.
"Learning and Discovery,"
Risk and Sustainable Management Group Working Papers
151174, University of Queensland, School of Economics.
- Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
- Halpern, Joseph Y., 2001.
"Alternative Semantics for Unawareness,"
Games and Economic Behavior,
Elsevier, vol. 37(2), pages 321-339, November.
- HEIFETZ, Aviad & MEIER, Martin & SCHIPPER, Burkhard C., 2004.
CORE Discussion Papers
2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2005. "Interactive Unawareness," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 52, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
- Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:503-525. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.