Studia Logica

, Volume 50, Issue 2, pp 251–260 | Cite as

Belief contraction without recovery

  • Sven Ove Hansson


The postulate of recovery is commonly regarded to be the intuitively least compelling of the six basic Gärdenfors postulates for belief contraction. We replace recovery by the seemingly much weaker postulate of core-retainment, which ensures that if x is excluded from K when p is contracted, then x plays some role for the fact that K implies p. Surprisingly enough, core-retainment together with four of the other Gärdenfors postulates implies recovery for logically closed belief sets. Reasonable contraction operators without recovery do not seem to be possible for such sets. Instead, however, they can be obtained for non-closed belief bases. Some results on partial meet contractions on belief bases are given, including an axiomatic characterization and a non-vacuous extension of the AGM closure condition.


Mathematical Logic Computational Linguistic Closure Condition Belief Base Contraction Operator 
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Copyright information

© Polish Academy of Sciences 1991

Authors and Affiliations

  • Sven Ove Hansson
    • 1
  1. 1.Department of PhilosophyUppsala UniversityUppsalaSweden

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