Skip to main content

Learning by Questions and Answers: From Belief-Revision Cycles to Doxastic Fixed Points

  • Conference paper
Book cover Logic, Language, Information and Computation (WoLLIC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5514))

Abstract

We investigate the long-term behavior of iterated belief revision with higher-level doxastic information. While the classical literature on iterated belief revision [13, 11] deals only with propositional information, we are interested in learning (by an introspective agent, of some partial information about the) answers to various questions Q 1, Q 2, ..., Q n , ... that may refer to the agent’s own beliefs (or even to her belief-revision plans). Here, “learning” can be taken either in the “hard” sense (of becoming absolutely certain of the answer) or in the “soft” sense (accepting some answers as more plausible than others). If the questions are binary (“is φ true or not?”), the agent “learns” a sequence of true doxastic sentences φ 1, ..., φ n , .... “Investigating the long-term behavior” of this process means that we are interested in whether or not the agent’s beliefs, her “knowledge” and her conditional beliefs stabilize eventually or keep changing forever.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. JSL 50, 510–530 (1985)

    MathSciNet  MATH  Google Scholar 

  2. Aucher, G.: A combined system for update logic and belief revision. Master’s thesis, ILLC, University of Amsterdam, Amsterdam, the Netherlands (2003)

    Google Scholar 

  3. Baltag, A., Moss, L.S.: Logics for epistemic programs. Synthese 139, 165–224 (2004); Knowledge, Rationality & Action 1–60

    Article  MathSciNet  MATH  Google Scholar 

  4. Baltag, A., Moss, L.S., Solecki, S.: The logic of common knowledge, public announcements, and private suspicions. In: Gilboa, I. (ed.) Proc. of TARK 1998, pp. 43–56 (1998)

    Google Scholar 

  5. Baltag, A., Smets, S.: Conditional doxastic models: a qualitative approach to dynamic belief revision. ENTCS 165, 5–21 (2006)

    MathSciNet  MATH  Google Scholar 

  6. Baltag, A., Smets, S.: The logic of conditional doxastic actions. Texts in Logic and Games 4, 9–32 (2008)

    MathSciNet  Google Scholar 

  7. Baltag, A., Smets, S.: A qualitative theory of dynamic interactive belief revision. Texts in Logic and Games 3, 9–58 (2008)

    MathSciNet  MATH  Google Scholar 

  8. van Benthem, J.F.A.K.: One is a lonely number. In: Koepke, P., Chatzidakis, Z., Pohlers, W. (eds.) Logic Colloquium 2002, pp. 96–129. ASL and A.K. Peter, Wellesley (2006)

    Google Scholar 

  9. van Benthem, J.F.A.K.: Dynamic logic of belief revision. JANCL 17(2), 129–155 (2007)

    MathSciNet  MATH  Google Scholar 

  10. Board, O.: Dynamic interactive epistemology. Games and Economic Behaviour 49, 49–80 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Booth, R., Meyer, T.: Admissible and restrained revision. Journal of Artificial Intelligence Research 26, 127–151 (2006)

    MathSciNet  MATH  Google Scholar 

  12. Boutilier, C.: Iterated revision and minimal change of conditional beliefs. JPL 25(3), 262–305 (1996)

    MathSciNet  MATH  Google Scholar 

  13. Darwiche, A., Pearl, J.: On the logic of iterated belief revision. Artificial Intelligence 89, 1–29 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. van Ditmarsch, H.P.: Prolegomena to dynamic logic for belief revision. Synthese 147, 229–275 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. van Ditmarsch, H.P., van der Hoek, W., Kooi, B.P.: Dynamic Epistemic Logic. Synthese Library, vol. 337. Springer, Heidelberg (2007)

    Book  MATH  Google Scholar 

  16. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  17. Grice, P.: Logic and conversation. In: Studies in the Ways of Words. Harvard University Press, Cambridge (1989)

    Google Scholar 

  18. Groenendijk, J., Stokhof, M.: Questions. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 1055–1124. Elsevier, Amsterdam (1997)

    Chapter  Google Scholar 

  19. Grove, A.: Two modellings for theory change. JPL 17, 157–170 (1988)

    MathSciNet  MATH  Google Scholar 

  20. Halpern, J.Y.: Reasoning about Uncertainty. MIT Press, Cambridge (2003)

    MATH  Google Scholar 

  21. Katsuno, H., Mendelzon, A.: On the difference between updating a knowledge base and revising it. Cambridge Tracts in Theoretical Computer Science, pp. 183–203 (1992)

    Google Scholar 

  22. Moore, G.E.: A reply to my critics. In: Schilpp, P.A. (ed.) The Philosophy of G.E. Moore. The Library of Living Philosophers, vol. 4, pp. 535–677. Northwestern University, Evanston (1942)

    Google Scholar 

  23. Nayak, A.C.: Iterated belief change based on epistemic entrenchment. Erkenntnis 41, 353–390 (1994)

    Article  MathSciNet  Google Scholar 

  24. Rott, H.: Conditionals and theory change: revisions, expansions, and additions. Synthese 81, 91–113 (1989)

    Article  MathSciNet  Google Scholar 

  25. 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, vol. II, pp. 105–134 (1988)

    Google Scholar 

  26. Veltman, F.: Defaults in update semantics. JPL 25, 221–261 (1996)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Baltag, A., Smets, S. (2009). Learning by Questions and Answers: From Belief-Revision Cycles to Doxastic Fixed Points. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2009. Lecture Notes in Computer Science(), vol 5514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02261-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02261-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02260-9

  • Online ISBN: 978-3-642-02261-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics