Advertisement

Reason to Believe

  • Chenwei Shi
  • Olivier Roy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10455)

Abstract

In this paper we study the relation between nonmonotonic reasoning and belief revision. Our main conceptual contribution is to suggest that nonmonotonic reasoning guides but does not determine an agent’s belief revision. To be adopted as beliefs, defeasible conclusions should remain stable in the face of certain bodies of information. This proposal is formalized in what we call a two-tier semantics for nonmonotonic reasoning and belief revision. The main technical result is a sound and complete axiomatization for this semantic.

References

  1. 1.
    Aucher, G.: A combined system for update logic and belief revision. Master’s thesis, ILLC, University of Amsterdam (2003)Google Scholar
  2. 2.
    Baltag, A., Smets, S.: A qualitative theory of dynamic interactive belief revision. Texts Log. Games 3, 9–58 (2008)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Boutilier, C.: Conditional logics of normality: a modal approach. Artif. Intell. 68, 87–154 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Boutilier, C.: Unifying default reasoning and belief revision in a modal framework. Artif. Intell. 68, 33–85 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.: Reasoning About Knowledge. MIT press, Cambridge (2004)zbMATHGoogle Scholar
  6. 6.
    Gärdenfors, P.: Belief revision and nonmonotonic logic: two sides of the same coin? In: Logics in AI, pp. 52–54 (1991)Google Scholar
  7. 7.
    Gärdenfors, P. (ed.): Belief Revision, vol. 29. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  8. 8.
    Gilbert, H.: Change in View. MIT Press, Cambridge (1986)Google Scholar
  9. 9.
    Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1), 167–207 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Leitgeb, H.: The stability theory of belief. Philos. Rev. 123(2), 131–171 (2014)CrossRefGoogle Scholar
  11. 11.
    Lin, H., Kelly, K.T.: Propositional reasoning that tracks probabilistic reasoning. J. Philos. Log. 41(6), 957–981 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Makinson, D.: Five faces of minimality. Stud. Log. 52(3), 339–379 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Rott, H.: Stability, strength and sensitivity: converting belief into knowledge. Erkenntnis 61(2–3), 469–493 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper, W.L., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics, pp. 105–134. Springer, Netherlands (1988)CrossRefGoogle Scholar
  15. 15.
    Van Ditmarsch, H.P.: Prolegomena to dynamic logic for belief revision. In: van der Hoek, W. (ed.) Uncertainty, Rationality, and Agency, pp. 175–221. Springer, Netherlands (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.ILLCUniversity of AmsterdamAmsterdamthe Netherlands
  2. 2.Universität BayreuthBayreuthGermany

Personalised recommendations