Revising and updating using a back-up semantics

  • Cees Witteveen
  • Wiebe van der Hoek
Belief Revision and Paraconsistency
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1126)


We introduce a novel approach to revision and updating where two semantics are used for the same class of theories. One semantics, the intended semantics, is used to give a theory its intended meaning, while the other, the back-up semantics, is used as a fall back whenever the intended semantics fails to provide a meaning to the theory.

Almost nothing will be assumed about the exact properties of both the intended and the back-up semantics, except for the following relations between them: (i) the entailment relation based on the intended semantics is stronger than the entailment relation based on the back-up semantics and (ii) the back-up semantics is defined for a broader class of theories than the intended semantics.

If, for some theory T, the intended semantics is not defined, revision of the theory is asked for. Like in the framework of classical theory revision, we apply revision by transforming the current theory T to another theory T′ such that the intended semantics is defined for T′. In that case, the back-up semantics is used to guarantee that as far as this latter semantics concerns, there is no loss in inferential power in transforming T to T′. Using this framework we develop some fairly intuitive postulates for (nonmonotonic) belief revision and updating. Together with some well-known abstract properties of entailment relations we then investigate which theory transformations are suitable for doing revision and updating of (nonmonotonic) theories. The main conclusions of this paper are:
  1. 1.

    In general, for revision, retraction is not suitable and, in many cases, minimal revision can only be achieved by applying revision by expansion.

  2. 2.

    When dealing with updating, retraction is not suitable for most nonmonotonic semantics. Even for nontrivial deletions, retracting information will not suffice if the back-up semantics satisfies some additional abstract properties.


We conclude by showing that this framework offers a possibility for refining some existing approaches to revision of nonmonotonic theories.


Theory Revision Updating Nonmonotonic Reasoning 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Cees Witteveen
    • 1
    • 2
  • Wiebe van der Hoek
    • 2
  1. 1.Department of Mathematics and Computer ScienceDelft University of TechnologyAJ DelftThe Netherlands
  2. 2.Department of Computer ScienceUtrecht UniversityCH UtrechtThe Netherlands

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