Skip to main content
SpringerLink
Log in

System of Spheres-based Multiple Contractions

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

We propose a new class of multiple contraction operations — the system of spheres-based multiple contractions — which are a generalization of Grove’s system of spheres-based (singleton) contractions to the case of contractions by (possibly non-singleton) sets of sentences. Furthermore, we show that this new class of functions is a subclass of the class of the partial meet multiple contractions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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). Amsterdam: Reidel.

    Chapter  Google Scholar 

  2. 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.

    Article  Google Scholar 

  3. Fermé, E., Saez, K., Sanz, P. (2003). Multiple kernel contraction. Studia Logica, 73, 183–195.

    Article  Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  10. Reis, M. D. L., & Fermé, E. (2011). Possible worlds semantics for partial meet multiple contraction. Journal of Philosophical Logic. doi:10.1007/s10992-011-9198-y.

    Google Scholar 

  11. Spohn, W. (2010). Multiple contraction revisited. In M. Suárez, M. Dorato, & M. Rédei (Eds.), EPSA epistemology and methodology of science (pp. 279–288). Netherlands: Springer.

    Google Scholar 

  12. Zhang, D. (1996). Belief revision by sets of sentences. Journal of Computer Science and Technology, 11(2), 108–125.

    Article  Google Scholar 

  13. Zhang, D., & Foo, N. (2001). Infinitary belief revision. Journal of Philosophical Logic, 30(6), 525–570.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Madeira Interactive Technologies Institute, Universidade da Madeira, Funchal, Portugal

    Eduardo Fermé & Maurício D. L. Reis

  2. Centro de Ciências Exactas e da Engenharia, Universidade da Madeira, Funchal, Portugal

    Maurício D. L. Reis

Authors
  1. Eduardo Fermé
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maurício D. L. Reis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eduardo Fermé.

Additional information

M. 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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fermé, E., Reis, M.D.L. System of Spheres-based Multiple Contractions. J Philos Logic 41, 29–52 (2012). https://doi.org/10.1007/s10992-011-9197-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-011-9197-z

Keywords

Search

Navigation