Skip to main content
SpringerLink
Log in

Temporal Interaction of Information and Belief

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

The temporal updating of an agent’s beliefs in response to a flow of information is modeled in a simple modal logic that, for every date t, contains a normal belief operator B t and a non-normal information operator I t which is analogous to the ‘only knowing’ operator discussed in the computer science literature. Soundness and completeness of the logic are proved and the relationship between the proposed logic, the AGM theory of belief revision and the notion of plausibility is discussed.

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., Gärdenfors P., Makinson D. (1985). ‘On the logic of theory change: partial meet contraction and revision functions’. The Journal of Symbolic Logic 50: 510–530

    Article  Google Scholar 

  2. Battigalli P. (1996). ‘Strategic independence and perfect Bayesian equilibria’. Journal of Economic Theory 70: 201–234

    Article  Google Scholar 

  3. Blackburn, P., M. de Rijke and Y. Venema, Modal logic, Cambridge University Press, 2001.

  4. Board O. (2004). ‘Dynamic interactive epistemology’. Games and Economic Behavior 49: 49–80

    Article  Google Scholar 

  5. Bonanno G. (1993). ‘Rational belief equilibria’. Economic Notes 22: 430–463

    Google Scholar 

  6. Bonanno, G., ‘A simple modal logic for belief revision’, Synthese (and Knowledge, Rationality and Action) 147: 193–228, 2005. Reprinted in W. van der Hoek (ed.), Uncertainty, rationality and agency, Springer, 2006, pp. 139–174.

  7. Bonanno, G., ‘Belief revision in a branching-time temporal framework’, Working Paper, University of California, Davis, 2006.

  8. Chellas, B., Modal logic: an introduction, Cambridge University Press, 1984.

  9. Friedman N., Halpern J. (1999). ‘Belief revision: a critique’. Journal of Logic, Language, and Information 8: 401–420

    Article  Google Scholar 

  10. Fudenberg D., Tirole J. (1991). ‘Perfect Bayesian equilibrium and sequential equilibrium’. Journal of Economic Theory 53: 236–260

    Article  Google Scholar 

  11. Gärdenfors, P., Knowledge in flux: modeling the dynamics of epistemic states, MIT Press, 1988.

  12. Goranko V., Passy S. (1992). ‘Using the universal modality: gains and questions’. Journal of Logic and Computation 2: 5–30

    Article  Google Scholar 

  13. Grove A. (1988). ‘Two modellings for theory change’. Journal of Philosophical Logic 17: 157–170

    Article  Google Scholar 

  14. Hintikka, J., Knowledge and belief, Cornell University Press, 1962.

  15. Katsuno, H., and A. O. Mendelzon, ‘On the difference between updating a knowledge and revising it’, in P. Gärdenfors (ed.), Belief Revision, Vol. 29 in Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 1992, pp. 83–203.

  16. Kreps, D., and R. Wilson, ‘Sequential equilibria’, Econometrica 50: 863–894.

  17. Kripke S. (1963). ‘A semantical analysis of modal logic I: normal propositional calculi’. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9: 67–96

    Article  Google Scholar 

  18. Levesque H.J. (1990). ‘All I know: a study in autoepistemic logic’. Artificial Intelligence 5: 263–309

    Article  Google Scholar 

  19. Nayak A., Pagnucco M., Peppas P. (2003). ‘Dynamic belief revision operators’. Artificial Intelligence 146: 193–228

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, University of California, Davis, CA, 95616, USA

    Giacomo Bonanno

Authors
  1. Giacomo Bonanno
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giacomo Bonanno.

Additional information

A first draft of this paper was presented at the Workshop on Belief Change in Rational Agents: Perspectives from Artificial Intelligence, Philosophy and Economics, Dagstuhl (Germany), August 2005.

Special Issue Formal Epistemology II. Edited by Branden Fitelson

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bonanno, G. Temporal Interaction of Information and Belief. Stud Logica 86, 375–401 (2007). https://doi.org/10.1007/s11225-007-9066-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-007-9066-5

Keywords

Search

Navigation