Relevance, recovery and recuperation: a prelude to ring withdrawal

Eduardo Fermé*, Marco Garapa, Abhaya Nayak, Maurício D.L. Reis

*Corresponding author for this work

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In this paper, we introduce recuperative withdrawals, belief change operators that satisfy recuperation, a postulate weaker than recovery, all the AGM postulates for contraction except recovery and another postulate which is a slightly stronger condition than conjunctive inclusion. Furthermore, we present a constructive definition for a class of operators —named ring withdrawals— which are such that the outcome of a ring withdrawal of a belief set K by a sentence α is obtained by adding to the set of most plausible models ‖K‖ all the worlds which are as close to ‖K‖ as its closest ¬α-worlds. Ring withdrawals satisfy the Lindström and Rabinowicz's interpolation thesis. We show that the classes of recuperative withdrawals and of ring withdrawals are identical. Additionally we show that the class of ring withdrawals is not contained in and does not contain the class of AGM contractions or the class of severe withdrawals. Finally we present methods for defining an operator of ring withdrawal by means of a severe withdrawal operator and by means of an AGM contraction operator, and vice-versa.

Original languageEnglish
Article number109108
Pages (from-to)1-21
Number of pages21
JournalInternational Journal of Approximate Reasoning
Publication statusPublished - Mar 2024

Bibliographical note

Copyright the Author(s) 2023. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • Belief contraction
  • Recovery postulate
  • Groove's system of spheres
  • Axiomatic characterization


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