Journal of Logic, Language and Information

, Volume 2, Issue 4, pp 255–284 | Cite as

Changes of disjunctively closed bases

  • Sven Ove Hansson


An operator of contraction for a belief set (a theory) can be obtained by assigning to it a belief base and an operator of partial meet contraction for that base. It is argued that closure of the base under disjunction is an intuitively reasonable condition. Axiomatic characterizations are given of the contractions of belief sets that can be generated by (various types of) partial meet contraction on disjunctively closed bases. The corresponding revision operators are also characterized. Finally, some results are reported on operations on bases that are closed under material implication.

Key words

AGM theory belief bases belief revision contraction database updating disjunctive closure Gärdenfors postulates partial meet contraction recovery postulate 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alchourrón, C.E., Gärdenfors, P. and Makinson, D., 1985, “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions,”Journal of Symbolic Logic 50, 510–530.Google Scholar
  2. Alchourrón, C.E., and Makinson, D., 1982, “On the Logic of Theory Change: Contraction Functions And Their Associated Revision Functions,”Theoria 48, 14–37.Google Scholar
  3. Fuhrmann, A., 1991, “Theory contraction through base contraction,”Journal of Philosophical Logic20, 175–203.Google Scholar
  4. Gärdenfors, P., 1988,Knowledge in Flux: Modeling the Dynamics of Epistemic States, Cambridge, MA: The MIT Press, Bradford Books.Google Scholar
  5. Ginsberg, M.L. and Smith, D.E., 1988, “Reasoning about Action I,”Artificial Intelligence 35, 165–195.Google Scholar
  6. Hansson, S.O., 1989, “New Operators For Theory Change,”Theoria 55, 114–132.Google Scholar
  7. Hansson, S.O., 1991, “Belief Contraction Without Recovery,”Studia Logica 50, 251–260.Google Scholar
  8. Hansson, S.O., 1992a, “In Defense of Base Contraction,”Synthese 91, 239–245.Google Scholar
  9. Hansson, S.O., 1992b, “A Dyadic Representation of Belief,” pp. 89–121 inBelief Revision, P. Gärdenfors, ed., Cambridge: Cambridge University Press.Google Scholar
  10. Hansson, S.O., 1992c, “Reversing the Levi Identity,”Journal of Philosophical Logic, in press.Google Scholar
  11. Hansson, S.O., 1992d, “Theory Contraction and Base Contraction Unified,”Journal of Symbolic Logic, in press.Google Scholar
  12. Makinson, D., 1987, “On the status of the postulate of recovery in the logic of theory change,”Journal of Philosophical Logic 16, 383–394.Google Scholar
  13. Nayak, A.C., 1992, “Foundational belief change,”Journal of Philosophical Logic, in press.Google Scholar
  14. Nebel, B., 1989, “A Knowledge Level Analysis of Belief Revision,” pp. 301–311 inPrinciples of Knowledge Representation and Reasoning, Proceedings of the 1st International Conference, Ronald Brachman, Hector Levesque and Raymond Reiter, eds., San Mateo, CA: Morgan Kaufmann.Google Scholar
  15. Nebel, B., 1992, “Syntax-Based Approaches to Belief Revision,” pp. 52–88 inBelief Revision, Peter Gärdenfors, ed., Cambridge: Cambridge University Press.Google Scholar
  16. Rott, H., 1992a, “Belief Contraction in the Context of the General Theory of Rational Choice,”Journal of Symbolic Logic, in press.Google Scholar
  17. Rott, H., 1992b, “Modelings for Belief Change: Prioritization and Entrenchment,”Theoria, in press.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Sven Ove Hansson
    • 1
  1. 1.Department of Philosophy Villavägen 5Uppsala UniversityUppsalaSweden

Personalised recommendations