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Possible Worlds Semantics for Partial Meet Multiple Contraction

Abstract

In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this paper we present the possible worlds semantics for partial meet multiple contractions.

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References

  1. 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.

  2. 2.

    Alchourrón, C., & Makinson, D. (1981). Hierarchies of regulations and their logic. In R. Hilpinen (Ed.), New studies in deontic logic: Norms, actions, and the foundations of ethics (pp. 125–148). D. Reidel Publishing Company.

  3. 3.

    Alchourrón, C., & Makinson, D. (1982). On the logic of theory change: Contraction functions and their associated revision functions. Theoria, 48, 14–37.

  4. 4.

    Chellas, B. F. (1980). Modal logic: An introduction. Cambridge University Press.

  5. 5.

    Fermé, E. & Reis, M. D. L. System of spheres-based multiple contractions. Journal of Philosophical Logic (this issue).

  6. 6.

    Fuhrmann, A. (1988). Relevant logics, modal logics and theory change. PhD thesis, Australian National University, Camberra.

  7. 7.

    Fuhrmann, A. (1991). Theory contraction through base contraction. Journal of Philosophical Logic, 20, 175–203.

  8. 8.

    Fuhrmann, A., & Hansson, S. O. (1994). A survey of multiple contraction. Journal of Logic, Language and Information, 3, 39–74.

  9. 9.

    Gärdenfors, P. (1982). Rules for rational changes of belief. In T. Pauli (Ed.), Philosophical essays dedicated to Lennart Ȧqvist on his fiftieth birthday (No. 34, pp. 88–101). Philosophical Studies.

  10. 10.

    Gärdenfors, P. (1988). Knowledge in flux: Modeling the dynamics of epistemic states. Cambridge: The MIT Press.

  11. 11.

    Gärdenfors, P., & Makinson, D. (1988). Revisions of knowledge systems using epistemic entrenchment. In M. Y. Vardi (Ed.), Proceedings of the second conference on theoretical aspects of reasoning about knowledge (pp. 83–95). Los Altos: Morgan Kaufmann.

  12. 12.

    Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17, 157–170.

  13. 13.

    Hansson, S. O. (1989). New operators for theory change. Theoria, 55, 114–132.

  14. 14.

    Hansson, S. O. (1991). Belief base dynamics. PhD thesis, Uppsala University.

  15. 15.

    Hansson, S. O. (1999). A Textbook of belief dynamics. Theory change and database updating. Applied logic series (Vol. 11). Dordrecht: Kluwer Academic Publishers.

  16. 16.

    Niederée, R. (1991). Multiple contraction: A further case against Gärdenfors’ principle of recovery. In A. Fuhrmann & M. Morreau (Eds.), The Logic of theory change (pp. 322–334). Berlin: Springer-Verlag.

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Author information

Correspondence to Maurício D. L. Reis.

Additional information

Maurício D. L. Reis was supported by Fundação para a Ciência e a Tecnologia (FCT) through the grant SFRH/BD/30175/2006 financed by national funds from Ministério da Ciência, Tecnologia e Ensino Superior (MCTES) from Portugal.

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Reis, M.D.L., Fermé, E. Possible Worlds Semantics for Partial Meet Multiple Contraction. J Philos Logic 41, 7–28 (2012). https://doi.org/10.1007/s10992-011-9198-y

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Keywords

  • Belief change
  • Theory contraction
  • Multiple contraction
  • Possible worlds semantics