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Impossibility results for belief contraction

  • Sven Ove HanssonEmail author
Open Access
Article

Abstract

Three seemingly weak and plausible conditions on an operation of contraction on belief sets are shown to be logically incompatible: (1) there is at least one sentence that can be successfully removed by the operation, (2) both the original belief set and the outcome of the operation have finite representations, and (3) a non-tautologous sentence can be removed without loss of all its non-tautologous logical consequences.

Keywords

Belief change Contraction Eradication Success postulates Finite-based outcome 

Mathematics Subject Classification (2010)

03B42 

Notes

References

  1. 1.
    Alchourrón, C., Makinson, D., Gärdenfors, P.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Log. 50, 510–530 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alchourrón, C., Makinson, D.: On the logic of theory change: Contraction functions and their associated revision functions. Theoria 48(1), 14–37 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Fermé, E., Hansson, S.O.: Shielded contraction. In: Rott, H., Williams, M.-A. (eds.) Frontiers of Belief Revision, pp 85–107 . Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
  4. 4.
    Fermé, E., Hansson, S.O.: Belief Change. Introduction and Overview. Springer, Berlin (2018)CrossRefGoogle Scholar
  5. 5.
    Gärdenfors, P., Makinson, D.: Revisions of knowledge systems using epistemic entrenchment. In: Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning about Knowledge, pp 83–95. Morgan Kaufmann Publishers, Los Angeles (1988)Google Scholar
  6. 6.
    Hansson, S.O.: Theory contraction and base contraction unified. J. Symb. Log. 58, 602–625 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hansson, S.O.: A Textbook of Belief Dynamics. Theory Change and Database Updating. Kluwer, Dordrecht (1999)CrossRefzbMATHGoogle Scholar
  8. 8.
    Hansson, S.O.: In praise of full meet contraction. Análisis Filosófico 26, 134–146 (2006)Google Scholar
  9. 9.
    Hansson, S.O.: Specified meet contraction. Erkenntnis 69, 31–54 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hansson, S.O.: Eradication. J. Appl. Log. 10, 75–84 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hansson, S.O.: Finite contractions on infinite belief sets. Stud. Logica. 100, 907–920 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Hansson, S.O., Wassermann, R.: Local change. Stud. Logica. 70, 49–76 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Makinson, D.: On the status of the postulate of recovery in the logic of theory change. J. Philos. Log. 16(4), 383–394 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Makinson, D.: Screened revision. Theoria 63, 14–23 (1997)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Parikh, R.: Beliefs, belief revision, and splitting languages, pp. 266-278 in Lawrence S. Moss, Jonathan Ginzburg, and Maarten de Rijke (eds) Logic, language, and computation, vol 2, CSLI lecture notes 96. Stanford, CA: CSLI (1999)Google Scholar
  16. 16.
    Rott, H.: Preferential belief change using generalized epistemic entrenchment. J. Log. Lang. Inf. 1(1), 45–78 (1992)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Kungliga Tekniska HögskolanStockholmSweden

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