Journal of Logic, Language and Information

, Volume 22, Issue 1, pp 1–21 | Cite as

Repertoire Contraction



The basic assumption of repertoire contraction is that only some of the logically closed subsets of the original belief set are viable as contraction outcomes. Contraction takes the form of choosing directly among these viable outcomes, rather than among cognitively more far-fetched objects such as possible worlds or maximal consistent subsets of the original belief set. In this first investigation of repertoire contraction, postulates for various variants of the operation are introduced. Necessary and sufficient conditions are given for when repertoire contraction coincides with AGM contraction or with operations generated by AGM-style contraction on a belief base. A close connection is shown to hold between repertoire contraction and specified meet contraction.


Repertoire contraction Outcome set AGM Specified meet contraction Partial meet contraction Full meet contraction Maxichoice contraction Kernel contraction Base-generated operations 



I would like to thank two anonymous referees for unusually detailed and useful comments on an earlier version of this paper.


  1. Alchourrón, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision function. Journal of Symbolic Logic, 50, 510–530.Google Scholar
  2. Alchourrón, C., & Makinson, D. (1981). Hierarchies of regulation and their logic. In R. Hilpinen (Ed.), New studies in deontic logic (pp. 125–148). Dordrecht: Reidel.Google Scholar
  3. Alchourrón, C., & Makinson, D. (1982). On the logic of theory change: contraction functions and their associated revision functions. Theoria, 48, 14–37.CrossRefGoogle Scholar
  4. Fermé, E., & Hansson, S. O. (2001). Shielded contraction. In H. Rott & M.-A. Williams (eds.) Frontiers of belief revision (pp. 85–107). Dordrecht: Kluwer.Google Scholar
  5. Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17, 157–170.CrossRefGoogle Scholar
  6. Hansson, S. O. (1989). New operators for theory change. Theoria, 55, 114–132.CrossRefGoogle Scholar
  7. Hansson, S. O. (1991). Belief contraction without recovery. Studia Logica, 50, 251–260.CrossRefGoogle Scholar
  8. Hansson, S. O. (1993). Theory contraction and base contraction unified. Journal of Symbolic Logic, 58, 602–625.CrossRefGoogle Scholar
  9. Hansson, S. O. (1994). Kernel contraction. Journal of Symbolic Logic, 59, 845–859.CrossRefGoogle Scholar
  10. Hansson, S. O. (1995). Some solved and unsolved remainder equations. Mathematical Logic Quarterly, 41, 362–368.Google Scholar
  11. Hansson, S. O. (1999). A textbook of belief dynamics. Theory change and database updating. Dordrecht: Kluwer.CrossRefGoogle Scholar
  12. Hansson, S. O. (2007). Contraction based on sentential selection. Journal of Logic and Computation, 17, 479–498.CrossRefGoogle Scholar
  13. Hansson, S. O. (2008). Specified meet contraction. Erkenntnis, 69, 31–54.CrossRefGoogle Scholar
  14. Hansson, S. O. (2012a, in press). Outcome level analysis of belief contraction. Review of Symbolic Logic.Google Scholar
  15. Hansson, S. O. (2012b, in press). Maximal and perimaximal contraction. Synthese.Google Scholar
  16. Hansson, S. O. (2012c, in press). Blockage contraction. Journal of Philosophical Logic.Google Scholar
  17. Hansson, S. O. (2012d, in press). Bootstrap contraction. Studia Logica.Google Scholar
  18. Olsson, E. J. (1998). Making beliefs coherent. The subtraction and addition strategies. Journal of Language, Logic, and Information, 7, 143–163.CrossRefGoogle Scholar
  19. Rott, H. (2001). Change, choice and inference: A study of belief revision and nonmonotonic reasoning. Oxford: Clarendon Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.KTH, Royal Institute of TechnologyStockholmSweden

Personalised recommendations