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International Conference on Scalable Uncertainty Management

SUM 2012: Scalable Uncertainty Management pp 219–232Cite as

Revision over Partial Pre-orders: A Postulational Study

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7520)

Abstract

Belief revision is the process that incorporates, in a consistent way, a new piece of information, called input, into a belief base. When both belief bases and inputs are propositional formulas, a set of natural and rational properties, known as AGM postulates, have been proposed to define genuine revision operations. This paper addresses the following important issue : How to revise a partially pre-ordered information (representing initial beliefs) with a new partially pre-ordered information (representing inputs) while preserving AGM postulates? We first provide a particular representation of partial pre-orders (called units) using the concept of closed sets of units. Then we restate AGM postulates in this framework by defining counterparts of the notions of logical entailment and logical consistency. In the second part of the paper, we provide some examples of revision operations that respect our set of postulates. We also prove that our revision methods extend well-known lexicographic revision and natural revision for both cases where the input is either a single propositional formula or a total pre-order.

Keywords

  • Epistemic State
  • Belief Revision
  • Belief Base
  • Belief Change
  • Propositional Formula

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-33362-0_17
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Author information

Authors and Affiliations

  1. School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast, BT7 1NN, UK

    Jianbing Ma & Weiru Liu

  2. CRIL-CNRS, UMR 8188, Faculté Jean Perrin, Université d’Artois, rue Jean Souvraz, 62307, Lens, France

    Salem Benferhat

Authors
  1. Jianbing Ma
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  2. Salem Benferhat
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  3. Weiru Liu
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Marburg University, Hans-Meerwein-Strasse 6, 35032, Marburg, Germany

    Eyke Hüllermeier, Thomas Fober & Bernhard Seeger,  & 

  2. Department of Computer Science, Auckland University, 38 Princes St., 1010, Auckland, New Zealand

    Sebastian Link

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Ma, J., Benferhat, S., Liu, W. (2012). Revision over Partial Pre-orders: A Postulational Study. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_17

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  • DOI: https://doi.org/10.1007/978-3-642-33362-0_17

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