IDEAS home Printed from https://ideas.repec.org/p/cda/wpaper/376.html

The logic of KM belief update is contained in the logic of AGM belief revision

Author

Listed:
  • Giacomo Bonanno

    (Department of Economics, University of California Davis)

Abstract

For each axiom of KM belief update we provide a corresponding axiom in a modal logic containing three modal operators: a unimodal belief operator $B$, a bimodal conditional operator $>$ and the unimodal necessity operator $\square$. We then compare the resulting logic to the similar logic obtained from converting the AGM axioms of belief revision into modal axioms and show that the latter contains the former. Denoting the latter by L_{AGM} and the former by L_{KM} we show that every axiom of L_{KM} is a theorem of L_{AGM} . Thus AGM belief revision can be seen as a special case of KM belief update. For the strong version of KM belief update we show that the difference between L_{KM} and L_{AGM} can be narrowed down to a single axiom, which deals exclusively with unsurprising information, that is, with formulas that were not initially disbelieved.

Suggested Citation

  • Giacomo Bonanno, 2026. "The logic of KM belief update is contained in the logic of AGM belief revision," Working Papers 376, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:376
    as

    Download full text from publisher

    File URL: https://repec.dss.ucdavis.edu/files/zjwl7ra3izse25oczizdvw7zbjml/KM_modal.pdf
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

    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:cda:wpaper:376. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Letters and Science IT Services Unit (email available below). General contact details of provider: https://edirc.repec.org/data/educdus.html .

    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.