IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v65y2013i2p73-84.html
   My bibliography  Save this article

Reasoning about knowledge of unawareness revisited

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489612000819
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2012.08.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, December.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. Joseph Y. Halpern & Evan Piermont, 2020. "Dynamic Awareness," Papers 2007.02823, arXiv.org.
    4. Gaia Belardinelli & Rasmus K. Rendsvig, 2020. "Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model," Papers 2012.12982, 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. 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.
    7. Piermont, Evan, 2017. "Introspective unawareness and observable choice," Games and Economic Behavior, Elsevier, vol. 106(C), pages 134-152.
    8. Gaia Belardinelli & Rasmus K. Rendsvig, 2021. "Awareness Logic: Kripke Lattices as a Middle Ground between Syntactic and Semantic Models," Papers 2106.12868, arXiv.org.
    9. Evan Piermont, 2023. "Iterated Revelation: How to Incentive Experts to Complete Incomplete Contracts," Papers 2304.05142, arXiv.org, revised Mar 2024.
    10. 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.
    11. 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.
    12. Patrick H. O'Callaghan, 2019. "Second-order Inductive Inference: an axiomatic approach," Papers 1904.02934, arXiv.org, revised Mar 2021.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    2. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    3. Burkhard Schipper, 2010. "Revealed Unawareness," Working Papers 303, University of California, Davis, Department of Economics.
    4. 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.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    6. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    7. Burkhard Schipper, 2011. "Preference-Dependent Unawareness," Working Papers 269, University of California, Davis, Department of Economics.
    8. Galanis, Spyros, 2018. "Speculation under unawareness," Games and Economic Behavior, Elsevier, vol. 109(C), pages 598-615.
    9. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
    10. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
    11. 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.
    12. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    13. Feinberg, Yossi, 2012. "Games with Unawareness," Research Papers 2122, Stanford University, Graduate School of Business.
    14. Fukuda, Satoshi, 2021. "Unawareness without AU Introspection," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    15. 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.
    16. Schipper, Burkhard C, 2010. "Revealed Unawareness," MPRA Paper 21491, University Library of Munich, Germany.
    17. Gaia Belardinelli & Burkhard C. Schipper, 2023. "Implicit Knowledge in Unawareness Structures," Working Papers 360, University of California, Davis, Department of Economics.
    18. Oliver Board, 2008. "Object-Based Unawareness: Theory and Applications," Working Paper 378, Department of Economics, University of Pittsburgh, revised Mar 2009.
    19. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    20. Spyros Galanis, 2013. "Unawareness of theorems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 41-73, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:65:y:2013:i:2:p:73-84. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.