Skip to main content
SpringerLink
Log in

Contracting Intuitionistic Theories

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

I reformulate the AGM-account of contraction (which would yield an account also of revision). The reformulation involves using introduction and elimination rules for relational notions. Then I investigate the extent to which the two main methods of partial meet contraction and safe contraction can be employed for theories closed under intuitionistic consequence.

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, CARLOS, PETER GÄRDENFORS, and DAVID MAKINSON, ‘On the logic of theory change: partial meet contractions and revision functions’, Journal of Symbolic Logic, 50:510–530, 1985.

    Google Scholar 

  2. ALCHOURRÓN, CARLOS, and DAVID MAKINSON, ‘On the logic of theory change: Safe contraction’, Studia Logica, 44:405–422, 1985.

    Article  Google Scholar 

  3. CHOPRA, SAMIR, JOHANNES HEIDEMA, and THOMAS MEYER, ‘Some logics of belief and disbelief’, in T.D. Gedeon and L. C. C. Fung, (eds.), AI 2003, LNAI 2903, pp. 364–376, Springer-Verlag, Berlin, Heidelberg, 2003.

    Google Scholar 

  4. FUHRMANN, ANDRÉ, An Essay on Contraction, CSLI Publications & FoLLI, 1997.

  5. FUHRMANN, ANDRÉ, ‘Theory contraction through base contraction’, Journal of Philosophical Logic, 20(2):175–203, 1991.

    Article  Google Scholar 

  6. GÄRDENFORS, PETER, Knowledge in Flux, MIT Press, Cambridge, MA, 1988.

    Google Scholar 

  7. LAKEMEYER, GERHARD, and WILFRIED LANG, ‘Belief revision in a nonclassical logic’, Künstliche Intelligenz, 20:199–211, 1996.

    Google Scholar 

  8. LINDSTRÖM, STEN, and WLODZIMIERZ RABINOWICZ, ‘On probabilistic representation of non-probabilistic belief-revision’, Journal of Philosophical Logic, 18(1):69–101, 1989.

    Article  Google Scholar 

  9. LINDSTRÖM, STEN, and WLODZIMIERZ RABINOWICZ, ‘Epistemic entrenchment with incomparabilities and relational belief revision’, in A. Fuhrmann and M. Morreau, (eds.), The logic of theory change, volume 465 of Lecture Notes in Computer Science, pp. 93–126, Springer Verlag, Berlin, 1991.

    Google Scholar 

  10. MAKINSON, DAVID, ‘In Memoriam Carlos Eduardo Alchourrón’, Nordic Journal of Philosophical Logic, 1(1):3–10, 1996.

    Google Scholar 

  11. MAKINSON, DAVID, ‘Ways of Doing Logic: What was Different about AGM 1985?’ Journal of Logic and Computation, 13:3–13, 2001.

    Google Scholar 

  12. TENNANT, NEIL, ‘Theory-Contraction is NP-Complete’, The Logic Journal of the IGPL, 11(6):675–693, 2003.

    Article  Google Scholar 

  13. TENNANT, NEIL, ‘Expansion, Contraction and Revision: What is the Right Division of Labor in Theory-Dynamics?’. Unpublished typescript.

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, The Ohio State University, 230 North Oval Mall, Columbus, OH, 43210, USA

    Neil Tennant

Authors
  1. Neil Tennant
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Neil Tennant.

Additional information

I would like to thank the organisers, Heinrich Wansing, Sergei Odintsov and Yaroslav Shramko, of the Dresden Workshop on Constructive Negation, July 2–4, 2004, for providing the opportunity to present the ideas in this paper for the first time to a constructively critical audience. I am grateful to Sven Ove Hansson for useful comments on an earlier draft. A special note of thanks is owed also to Joongol Kim, who spotted a mistake in an earlier attempt of mine to prove a stronger form of Theorem 8.6. The results in this paper were presented to the Central Division Meeting of the American Philosophical Association in Chicago in April 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tennant, N. Contracting Intuitionistic Theories. Stud Logica 80, 369–391 (2005). https://doi.org/10.1007/s11225-005-8475-6

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-005-8475-6

Keywords

Search

Navigation