Skip to main content
SpringerLink
Log in

Dynamic Epistemic Logic

  • Chapter
  • First Online:
Book cover Reasoning about Preference Dynamics

Part of the book series: Synthese Library ((SYLI,volume 354))

  • 769 Accesses

Abstract

What is knowledge? How can we acquire knowledge? When can we say that we know something? Do we know that we know something? Those are the issues that puzzled Chinese philosophers about 2000 years ago, witness a famous dialogue below between Zhuangzi (approx.369–286 BC) from the Daoism School and Huizi (390–317 BC) from the School of Names: One day Zhuangzi and Huizi are strolling on Bridge Hao.

Zhuangzi: “Look how happy the fish are just swimming around in the river.”

Huizi: “How do you know they are happy? You are not a fish.”

Zhuangzi: “And you are not me. How do you know I don’t know the fish are happy?”

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    Reference [11] studied epistemic logic from both internal and external perspectives.

  2. 2.

    References [65] and [32] are two comprehensive and more up-to-date references.

  3. 3.

    In this book, possible states/worlds are denoted by variables w, v, s, t, but also sometimes x, y, as seems convenient in the statement of notions and proofs.

  4. 4.

    I have benefited from a discussion of this point with Johan van Benthem. His new book [32] contains a further analysis of this issue in terms of logical validities for various dynamic actions, and concrete illustrations in the context of games and protocol update.

  5. 5.

    Note that the pre-conditions in the event model are formalized in the dynamic epistemic language, this might introduce circularities. One solution is to “view the preconditions as literal parts of event models”. We refer to [32] and [65] for further dicussions.

  6. 6.

    In this book, we will not use the original privacy motivations for product update. In our later applications to qualitative and quantitative preference change, the different events are rather different “signals” that can apply to worlds, whose ordering tells us something about how agents are to evaluate their relative betterness or plausibility.

  7. 7.

    For a first programmatic discussion in this vein, see [29].

  8. 8.

    Say, with epistemic S5, the frame still has equivalence relations after DEL update.

  9. 9.

    Still, the reduction does not settle computational complexity: Translation via the axioms may increase formula length exponentially. Still, for the case of PAL, the complexity of satisfiability remains that of epistemic logic, viz. Pspace-complete (cf. [138]).

  10. 10.

    This again requires a reduction axiom for conditional common knowledge, which can be done as well. A good reference for such issues of language design in DEL is [34].

References

  1. Alchourrón, C., P. Gärdenfors, and D. Makinson. 1985. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50:510–530.

    Article  Google Scholar 

  2. Aucher, G. 2008. Perspectives on belief and change. PhD thesis, Université de Toulouse.

    Google Scholar 

  3. Baltag, A., L.S. Moss, and S. Solecki. 1998. The logic of common knowledge, public announcements, and private suspicions. In Proceedings of the 7th conference on theoretical aspects of rationality and knowledge (TARK 98), ed. I. Gilboa, 43–56. Morgan Kaufmann Publishers: San Francisco, CA, USA.

    Google Scholar 

  4. Baltag, A., and S. Smets. 2006. The logic of conditional doxastic actions: A theory of dynamic multi-agent belief revision. In Proceedings of the workshop on rationality and knowledge. eds. S. Artemov and R. Parikh, 13–30. Malaga: ESSLLI.

    Google Scholar 

  5. van Benthem, J. 2007. Dynamic logic for belief revision. Journal of Applied Non-Classical Logic 17:129–156.

    Article  Google Scholar 

  6. van Benthem, J. 2011. Logical dynamics of information and interaction. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  7. van Benthem, J., J. van Eijck, and B. Kooi. 2006. Logics of communication and change. Information and Computation 204:1620–1662.

    Article  Google Scholar 

  8. van Benthem, J., J. Gerbrandy, T. Hoshi, and E. Pacuit. 2009. Merging frameworks for interaction. Journal of Philosophical Logic 38(5):491–526.

    Article  Google Scholar 

  9. van Benthem, J., and S. Minica. 2009. Toward a dynamic logic of questions. In Proceedings of the 2nd international workshop on logic, rationality and interaction (LORI 2009), eds. X. He, J. Horty, and E. Pacuit, volume 5834 of FoLLI-LNAI, 27–41. Springer: Heidelberg.

    Chapter  Google Scholar 

  10. van Benthem, J. 2010. Modal logic for open minds. Stanford: CSLI Publications.

    Google Scholar 

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

    Google Scholar 

  12. Chisholm, R. 1982. The foundations of knowing. Minneapolis, MN: University of Minnesota Press.

    Google Scholar 

  13. Conee, E., and R. Feldman. 2004. Evidentialism. Essays in epistemology. Oxford: Oxford University Press.

    Google Scholar 

  14. van Ditmarsch, H., W. van der Hoek, and B. Kooi. 2007. Dynamic epistemic logic. Berlin: Springer.

    Google Scholar 

  15. Dretske, F. 1981. Knowledge and the flow of information. Oxford: Blackwell.

    Google Scholar 

  16. Fagin, R., J.Y. Halpern, Y. Moses, and M.Y. Vardi. 1995. Reasoning about knowledge. Cambridge, MA: The MIT Press.

    Google Scholar 

  17. Gerbrandy, J. 1999. Bisimulation on planet Kripke. PhD thesis, ILLC, University of Amsterdam.

    Google Scholar 

  18. Girard, P. 2008. Modal logics for belief and preference change. PhD thesis, Stanford University.

    Google Scholar 

  19. Goldman, A. 1991. Epistemic folkways and scientific epistemology. Liaisons: Philosophy Meets the Cognitive and Social Sciences. Cambridge, MA: The MIT Press.

    Google Scholar 

  20. Hoshi, T. 2009. Epistemic dynamics and protocol information. PhD thesis, Stanford University.

    Google Scholar 

  21. Hinttika, J. 1962. Knowledge and belief. Ithaca, NY: Cornell University Press.

    Google Scholar 

  22. Lewis, D. 1969. Convention: A philosophical study. Cambridge, MA: Harvard University Press.

    Google Scholar 

  23. Liu, F. 2008. Changing for the better: Preference dynamics and agent diversity. PhD thesis, ILLC, University of Amsterdam.

    Google Scholar 

  24. Lutz, C. 2006. Complexity and succinctness of public announcement logic. In Proceedings of the 5th international conference on autonomous agents and multiagent systems (AAMAS06), 137–144. IEEE/ACM Press: New York.

    Google Scholar 

  25. McCarthy, J. 1986. Circumscription – A form of non-monotonic reasoning. Artificial Intelligence 13:27–39.

    Article  Google Scholar 

  26. Meyer, J.-J.Ch. and W. van der Hoek. 1995. Epistemic logic for computer science and artificial intelligence. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  27. Nozick, R. 1981. Philosophical explanations. Cambridge, MA: Harvard University Press.

    Google Scholar 

  28. Plantinga, A. 1991. Knowledge in perspective. Selected essays in epistemology. Cambridge: Cambridge University Press.

    Google Scholar 

  29. Plaza, J.A. 1989. Logics of public communications. In Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, eds. M. Emrich, M. Pfeifer, M. Hadzikadic, Z. Ras, 201–216. Charlotte, North Carolina.

    Google Scholar 

  30. Aumann, R. 1976. Agreeing to disagree. Annals of Statistics 4:1236–1239.

    Article  Google Scholar 

  31. Reiter, R. 1980. A logic for default reasoning. Artificial Intelligence 13(1–2):81–132.

    Article  Google Scholar 

  32. Roy, O. 2008. Thinking before acting: Intentions, logic and rational choice. PhD thesis, ILLC, University of Amsterdam.

    Google Scholar 

  33. Steup, M., and E. Sosa, ed. 2005. Contemporary debates in epistemology. Cambridge, MA: Blackwell.

    Google Scholar 

  34. Velazquez-Quesada, F.R. 2011. Small steps in dynamics of information. PhD thesis, ILLC, University of Amsterdam.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, Tsinghua University, 100084, Beijing, Haidian District, China PRC

    Assoc. Prof. Fenrong Liu

Authors
  1. Assoc. Prof. Fenrong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fenrong Liu .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Liu, F. (2011). Dynamic Epistemic Logic. In: Reasoning about Preference Dynamics. Synthese Library, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1344-4_2

Download citation

Publish with us

Policies and ethics

Search

Navigation