Iterated Contraction Based on Indistinguishability

  • Konstantinos Georgatos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7734)


We introduce a class of set-theoretic operators on a tolerance space that models the process of minimal belief contraction, and therefore a natural process of iterated contraction can be defined. We characterize the class of contraction operators and study the properties of the associated iterated belief contraction.


Geodesic Distance Belief Revision Kripke Model Contraction Operator Contraction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zeeman, E.C.: The topology of the brain and visual perception. In: Fort, M.K. (ed.) The Topology of 3-Manifolds, pp. 240–256. Prentice Hall, Englewood Cliffs (1962)Google Scholar
  2. 2.
    Bell, J.L.: A new approach to quantum logic. The British Journal for the Philosophy of Science 37, 83–99 (1986)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Georgatos, K.: On indistinguishability and prototypes. Logic Journal of the IGPL 11(5), 531–545 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Georgatos, K.: Geodesic revision. Journal of Logic and Computation 19(3), 447–459 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Georgatos, K.: Conditioning by Minimizing Accessibility. In: Bonanno, G., Löwe, B., van der Hoek, W. (eds.) LOFT 2008. LNCS (LNAI), vol. 6006, pp. 20–33. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Lewis, D.: Counterfactuals. Harvard University Press, Cambridge (1973)Google Scholar
  7. 7.
    Williamson, T.: First-order logics for comparative similarity. Notre Dame Journal of Formal Logic 29, 457–481 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Hansson, S.O.: Similarity semantics and minimal changes of belief. Erkenntnis 37, 401–429 (1992)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lehmann, D.J., Magidor, M., Schlechta, K.: Distance semantics for belief revision. J. Symb. Log. 66(1), 295–317 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Rabinowicz, W.: Global belief revision based on similarities between worlds. In: Hansson, S.O., Rabinowicz, W. (eds.) Logic for a Change: Essays Dedicated to Sten Lindström on the Occasion of His Fiftieth Birthday. Uppsala prints and preprints in philosophy, vol. 9, pp. 80–105. Department of Philosophy, Uppsala University (1995)Google Scholar
  11. 11.
    Schlechta, K.: Non-prioritized belief revision based on distances between models. Theoria 63(1-2), 34–53 (1997)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. Journal of Symbolic Logic 50, 510–530 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Makinson, D.: On the status of the postulate of recovery in the logic of theory change. Journal of Philosophical Logic 16, 383–394 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Hansson, S.O.: Belief contraction without recovery. Studia Logica 50(2), 251–260 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Fermé, E.L.: On the logic of theory change: Contraction without recovery. Journal of Logic, Language and Information 7(2), 127–137 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Nayak, A.C., Goebel, R., Orgun, M.A.: Iterated belief contraction from first principles. In: Veloso, M.M. (ed.) IJCAI, pp. 2568–2573 (2007)Google Scholar
  17. 17.
    Hansson, S.O.: Multiple and iterated contraction reduced to single-step single-sentence contraction. Synthese 173(2), 153–177 (2010)zbMATHCrossRefGoogle Scholar
  18. 18.
    Nayak, A.C., Goebel, R., Orgun, M.A., Pham, T.: Taking Levi Identity Seriously: A Plea for Iterated Belief Contraction. In: Lang, J., Lin, F., Wang, J. (eds.) KSEM 2006. LNCS (LNAI), vol. 4092, pp. 305–317. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Tamminga, A.M.: Expansion and contraction of finite states. Studia Logica 76(3), 427–442 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Hansson, S.O.: Global and iterated contraction and revision: An exploration of uniform and semi-uniform approaches. J. Philosophical Logic 41(1), 143–172 (2012)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Konstantinos Georgatos
    • 1
    • 2
  1. 1.Department of Mathematics and Computer Science, John Jay CollegeCity University of New YorkNew YorkUSA
  2. 2.Doctoral Program in Computer Science, Graduate CenterCity University of New YorkNew YorkUSA

Personalised recommendations