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.
KeywordsMathematical Logic Computational Linguistic Closure Condition Belief Base Contraction Operator
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- C. E. Alchourrón, P. Gärdenfors and D. Makinson. On the logic of theory change: Partial meet functions for contraction and revision, Journal of Symbolic Logic 50 (1985), pp. 510–530.Google Scholar
- C. E. Alchourrón and D. Makinson, On the logic of theory change: Safe contraction, Studia Logica 44 (1985), pp. 405–422.Google Scholar
- M. Dalal, Investigations into a theory of knowledge base revision: Preliminary Report, Proceedings of the Seventh National Conference on Artificial Intelligence (1988), pp. 475–479.Google Scholar
- A. Fuhrmann, Theory contraction through base contraction, Journal of Philosophical Logic 20 (1991), pp. 175–203.Google Scholar
- P. Gärdenfors, Epistemic importance and minimal changes of belief, Australasian Journal of Philosophy 62 (1984), pp. 136–157.Google Scholar
- P. Gärdenfors, Knowledge in Flux. Modeling the Dynamics of Epistemic States, MIT Press, Cambridge 1988.Google Scholar
- S. O. Hansson, New operators for theory change, Theoria 50 (1989), pp. 114–132.Google Scholar
- S. O. Hansoon, A dyadic representation of belief,forthcoming in Peter Gärdenfors, Belief Revision, Cambridge University Press, Cambridge, 1991.Google Scholar
- S. O. Hansson, In defense of base contraction, Synthese (1991), in print.Google Scholar
- D. Makinson, On the status of the postulate of recovery in the logic of theory change, Journal of Philosophical Logic 16 (1987), pp. 383–394.Google Scholar
- R. Niederée, Multiple contraction. A further case against Gärdenfors' Principle of recovery, in A.Fuhrmann and M. Morreau (eds.), The Logic of Theory Change, Lecture Notes in Artificial Intelligence 465, 1991, pp. 322–334.Google Scholar