Studia Logica

, Volume 70, Issue 1, pp 23–47 | Cite as

Iterated Belief Revision and Conditional Logic

  • Laura Giordano
  • Valentina Gliozzi
  • Nicola Olivetti


In this paper we propose a conditional logic called IBC to represent iterated belief revision systems. We propose a set of postulates for iterated revision which are a small variant of Darwiche and Pearl's ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. We establish a correspondence between iterated belief revision systems and IBC-models. Our representation theorem does not entail Gärdenfors' Triviality Result.


Small Variant Mathematical Logic Selection Function Function Model Computational Linguistic 
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  1. [1]
    C. E. Alchourrón, P. Gärdenfors, D. Makinson, On the logic of theory change: partial meet contraction and revision functions, Journal of Symbolic Logic, 50:510-530, 1985.Google Scholar
  2. [2]
    C. Boutilier, Revision sequences and nested conditionals, in Proc. 13th International Joint Conference on Artificial Intelligence (IJCAI'93), Chambery, pp. 519-525.Google Scholar
  3. [3]
    A. Darwiche, J. Pearl, On the logic of iterated belief revision, Artificial Intelligence, 89:1-29, 1997.Google Scholar
  4. [4]
    N. Friedman, J. Y. Halpern, Conditional logics of belief change, in Proceedings of the National Conference on Artificial Intelligence (AAAI 94), pp. 915-921, 1994.Google Scholar
  5. [5]
    P. Gärdenfors, Knowledge in flux: modeling the dynamics of epistemic states, MIT Press, Cambridge, Massachussets, 1988.Google Scholar
  6. [6]
    L. Giordano, V. Gliozzi, N. Olivetti, A conditional logic for belief revision, in Proc. JELIA '98, LNAI 1489, Springer, 294-308, 1998.Google Scholar
  7. [7]
    L. Giordano, V. Gliozzi, N. Olivetti, A conditional logic for iterated belief revision, to appear in ECAI2000, Proc. 14th European Conference on Artificial Intelligence, W. Horn (ed.), IOS Press, Berlin, 2000, pp. 28-32.Google Scholar
  8. [8]
    G. Grahne, Updates and counterfactuals, Journal of Logic and Computation, Vol 8,No. 1:87-117, 1998.Google Scholar
  9. [9]
    H. Katsuno, A. O. Mendelzon, On the difference between updating a knowledge base and revising it, in Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, 1991.Google Scholar
  10. [10]
    H. Katsuno, K. Satoh, A unified view of consequence relation, belief revision and conditional logic, in Proc. 12th International Joint Conference on Artificial Intelligence (IJCAI'91), 1991, pp. 406-412.Google Scholar
  11. [11]
    D. Lehmann, Belief revision revised, in Proc. 14th International Joint Conference on Artificial Intelligence (IJCAI'95), 1995, pp. 1534-1540.Google Scholar
  12. [12]
    D. Lewis, Counterfactuals, Blackwell, 1973.Google Scholar
  13. [13]
    S. Lindström, W. Rabinowicz, The Ramsey test revisited, in Crocco, Fariñas del Cerro, Herzig (eds.) Conditionals from Philosophy to Computer Science, Oxford University Press, 1995.Google Scholar
  14. [14]
    W. Nejdl, M. Banagl, Asking about possibilities-revision and update semantics for subjunctive queries, in Lakemayer, Nebel, Foundations of Knowledge Representation and Reasoning, Lecture Notes in Artificial Intelligence 810: 250-274, 1994.Google Scholar
  15. [15]
    D. Nute, Topics in Conditional Logic, Reidel, Dordrecht, 1980.Google Scholar
  16. [16]
    F. P. Ramsey, in A. Mellor (editor), Philosophical Papers, Cambridge University Press, Cambridge, 1990.Google Scholar
  17. [17]
    M. D. Ryan and P.-Y. Schobbens, Counterfactuals and updates as inverse modalities, Journal of Logic, Language and Information, 6, pp. 123-146, 1997.Google Scholar
  18. [18]
    R. Stalnaker, A theory of conditionals, in N. Rescher (ed.), Studies in Logical Theory, American Philosophical Quarterly, Monograph Series no. 2, Blackwell, Oxford: 98-112, 1968.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Laura Giordano
    • 1
  • Valentina Gliozzi
    • 2
  • Nicola Olivetti
    • 2
  1. 1.DSTAUniversità del Piemonte Orientale "A. Avogadro"AlessandriaItaly
  2. 2.Dipartimento di InformaticaUniversità di TorinoTorinoItaly

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