Safe Contraction Revisited

  • Hans Rott
  • Sven Ove Hansson
Part of the Outstanding Contributions to Logic book series (OCTR, volume 3)


Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results and offers a list of unsolved problems that are in need of investigation.


Safe contraction Hierarchy AGM Epistemic entrenchment Kernel contraction Supplementary postulates  Iterated safe contraction Multiple safe contraction Non-prioritized safe contraction Safe revision 


  1. Alchourrón, C., Gärdenfors, P., & 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., & Makinson, D. (1985). On the logic of theory change: Safe contraction. Studia Logica, 44, 405–422.Google Scholar
  3. Alchourrón, C. E., & Makinson, D. (1986). Maps between some different kinds of contraction function: The finite case. Studia Logica, 45, 187–198.Google Scholar
  4. Areces, C., & Becher, V. (2001). Iterable AGM functions. In M.-A. Williams & H. Rott (Eds.), Frontiers in Belief Revision (pp. 261–277). Dordrecht: Kluwer.Google Scholar
  5. Besnard, P., & Hunter, A. (2008). Elements of Argumentation. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
  6. Carnota, R., & Rodríguez, R. (2011). AGM theory and artificial intelligence. In E. J. Olsson & S. Enqvist (Eds.), Belief Revision meets Philosophy of Science (pp. 1–42). Dordrecht: Springer.Google Scholar
  7. Falappa, M., Fermé, E., & Kern-Isberner, G. (2006). On the Logic of Theory Change: Relations Between Incision and Selection Functions. In G. Brewka et al. (eds.), ECAI’2006, 17th European Conference on Artificial Intelligence (pp. 402–406). IOS Press.Google Scholar
  8. Fermé, E., & Hansson, S. O. (2011). AGM 25 years of research in belief change. Journal of Philosophical Logic, 40, 295–331.Google Scholar
  9. Fermé, E., & Reis, M. (2012). System of spheres-based multiple contractions. Journal of Philosophical Logic, 41, 29–52.Google Scholar
  10. Fermé, E., Saez, K., & Sanz, P. (2003). Multiple kernel contraction. Studia Logica, 73, 183–195.CrossRefGoogle Scholar
  11. Fuhrmann, A., & Hansson, S. O. (1994). A survey of multiple contractions. Journal of Logic, Language, and Information, 3, 39–76.Google Scholar
  12. Gärdenfors, P. (1982). Rules for rational changes of belief. In T. Pauli (Ed.), \(\langle \)320311\(\rangle \): Philosophical Essays Dedicated to Lennart Åqvist on His Fiftieth Birthday, Vol. 34 (pp. 88–101). Uppsala: University of Uppsala Philosophical Studies.Google Scholar
  13. Gärdenfors, P. (1988). Knowledge in flux: Modeling the dynamics of epistemic states. Cambridge, MA: Bradford Books, MIT Press.Google Scholar
  14. Gärdenfors, P., & Makinson, D. (1988). Revisions of knowledge systems using epistemic entrenchment. In M. Vardi (Ed.), TARK’88: Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge (pp. 83–95). Los Altos, CA: Morgan Kaufmann.Google Scholar
  15. Hansson, S. O. (1989). New operators for theory change. Theoria, 55, 114–132.Google Scholar
  16. Hansson, S. O. (1992). A dyadic representation of belief. In P. Gärdenfors (Ed.), Belief Revision (pp. 89–121). Cambridge: Cambridge University Press.Google Scholar
  17. Hansson, S. O. (1993). Reversing the Levi identity. Journal of Philosophical Logic, 22, 637–669.Google Scholar
  18. Hansson, S. O. (1994). Kernel contraction. Journal of Symbolic Logic, 59, 845–859.Google Scholar
  19. Hansson, S. O. (1999a). A Textbook of Belief Dynamics. Theory Change and Database Updating. Dordrecht : Kluwer.Google Scholar
  20. Hansson, S. O. (1999b). A survey of non-prioritized belief revision. Erkenntnis, 50, 413–427.Google Scholar
  21. Hansson, S. O. (2010). Multiple and iterated contraction reduced to single-step single-sentence contraction. Synthese, 173, 153–177.Google Scholar
  22. Hansson, S. O. (2012). Global and iterated contraction and revision: An exploration of uniform and semi-uniform approaches. Journal of Philosophical Logic, 41, 143–172.Google Scholar
  23. Hansson, S. O., Fermé, E., Cantwell, J., & Falappa, M. (2001). Credibility-limited revision. Journal of Symbolic Logic, 66, 1581–1596.CrossRefGoogle Scholar
  24. Li, J. (1998). A note on partial meet package contraction. Journal of Logic, Language and Information, 7, 139–142.Google Scholar
  25. 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
  26. Makinson, D. (1989). General theory of cumulative inference. In M. Reinfrank, J. de Kleer, M. Ginsberg, & E. Sandewall (Eds.), Non-Monotonic Reasoning—Proceedings of the 2nd International Workshop Grassau, FRG, June 13–15, 1988 (pp. 1–18). Berlin: Springer.Google Scholar
  27. Makinson, D. (1997). Screened revision. Theoria, 63, 14–23.Google Scholar
  28. Reis, M., & Fermé, E. (2012). Possible worlds semantics for partial meet multiple contraction. Journal of Philosophical Logic, 41, 7–28.Google Scholar
  29. Rott, H. (1992a). On the logic of theory change: More maps between different kinds of contraction functions. In P. Gärdenfors (Ed.), Belief Revision (pp. 122–141). Cambridge: Cambridge University Press.Google Scholar
  30. Rott, H. (1992b). Preferential belief change using generalized epistemic entrenchment. Journal of Logic, Language and Information, 1, 45–78.CrossRefGoogle Scholar
  31. Rott, H. (1993). Belief contraction in the context of the general theory of rational choice. Journal of Symbolic Logic, 58, 1426–1450.CrossRefGoogle Scholar
  32. Rott, H. (1999). Coherence and conservatism in the dynamics of belief. Part I: Finding the right framework. Erkenntnis, 50, 387-412.Google Scholar
  33. Rott, H. (2000). Just because: Taking belief bases seriously. In S. R. Buss, P. Hájek, & P. Pudlák (Eds.), Logic Colloquium ’98—Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic held in Prague, Urbana (pp. 387–408). Urbana, Ill: Association for Symbolic Logic.Google Scholar
  34. Rott, H. (2001). Change, choice and inference: A study of belief revision and nonmonotonic reasoning. Oxford: Oxford University Press.Google Scholar
  35. Rott, H. (2003). Basic entrenchment. Studia Logica, 73, 257–280.CrossRefGoogle Scholar
  36. Sen, A. (1986). Social choice theory. In K. J. Arrow & M. D. Intriligator (Eds.), Handbook of Mathematical Economics (Vol. III, pp. 1073–1181). Amsterdam: Elsevier/North-Holland.Google Scholar
  37. Sen, A. (1997). Maximization and the act of choice. Econometrica, 65, 745–779.Google Scholar
  38. Spohn, W. (2010) Multiple contraction revisited. In M. Suárez, M. Dorato & M. Rédei (Eds.), EPSA Epistemology and Methodology of Science. Launch of the European Philosophy of Science Association, (Vol. 1, pp. 279–288). Dordrecht: Springer.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.University of RegensburgRegensburgGermany
  2. 2.Royal Institute of Technology (KTH)StockholmSweden

Personalised recommendations