IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4899-1424-8_7.html
   My bibliography  Save this book chapter

Revision Rules for Convex Sets of Probabilities

In: Mathematical Models for Handling Partial Knowledge in Artificial Intelligence

Author

Listed:
  • Serafín Moral

    (Universidad de Granada, Departamento de Ciencias de la Computacion)

  • Nic Wilson

    (Queen Mary and Westfield College, Department of Computer Science)

Abstract

The best understood and most highly developed theory of uncertainty is Bayesian probability. There is a large literature on its foundations and there are many different justifications of the theory; however, all of these assume that for any proposition a, the beliefs in a and ⌝a are strongly tied together. Without compelling justification, this assumption greatly restricts the type of information that can be satisfactorily represented, e.g., it makes it impossible to represent adequately partial information about an unknown chance distribution P such as 0.6 ≤ P(a) ≤ 0.8. The strict Bayesian requirement that an epistemic state be a single probability function seems unreasonable. A natural extension of the Bayesian theory is thus to allow sets of probability functions and to consider constraints and bounds on these, and to calculate supremum and infimum values of the probabilities of propositions (known as Upper and Lower Probabilities) given the constraints. Early work on this includes Boole1 and Good2 and early appearances in the Artificial Intelligence literature include Quinlan3 and Nilsson4.

Suggested Citation

  • Serafín Moral & Nic Wilson, 1995. "Revision Rules for Convex Sets of Probabilities," Springer Books, in: Giulianella Coletti & Didier Dubois & Romano Scozzafava (ed.), Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, pages 113-127, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1424-8_7
    DOI: 10.1007/978-1-4899-1424-8_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-1-4899-1424-8_7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.