Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Common Knowledge Revisited

  • Chapter
Knowledge Contributors

Part of the book series: Synthese Library ((SYLI,volume 322))

Abstract

We consider the common-knowledge paradox raised by Halpern and Moses: common knowledge is necessary for agreement and coordination, but common knowledge is unattainable in the real world because of temporal imprecision. We discuss two solutions to this paradox: (1) modeling the world with a coarser granularity, and (2) relaxing the requirements for coordination.

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 PDF
  • Read on any device
  • Instant download
  • Own it forever
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. J. Aumann. Agreeing to disagree. Annals of Statistics, 4(6):1236–1239, 1976.

    Article  Google Scholar 

  2. R. J. Aumann. Formal common knowledge: an approach to the Halpern-Moses problem. Manuscript, 1989.

    Google Scholar 

  3. J. Barwise. Scenes and other situations. Journal of Philosophy, 78(7):369–397, 1981.

    Article  Google Scholar 

  4. J. Barwise. Three views of common knowledge. In M. Y. Vardi, editor, Proc. Second Conference on Theoretical Aspects of Reasoning about Knowledge, pages 365–379. Morgan Kaufmann, San Francisco, Calif., 1988.

    Google Scholar 

  5. A. Brandenburger and E. Dekel. Common knowledge with probability 1. Journal of Mathematical Economics, 16:237–245, 1987.

    Article  Google Scholar 

  6. H. H. Clark and C. R. Marshall. Definite reference and mutual knowledge. In A. K. Joshi, B. L. Webber, and I. A. Sag, editors, Elements of discourse understanding. Cambridge University Press, Cambridge, U.K., 1981.

    Google Scholar 

  7. D. Dolev, J. Y. Halpern, and H. R. Strong. On the possibility and impossibility of achieving clock synchronization. Journal of Computer and System Sciences, 32(2):230–250, 1986.

    Article  Google Scholar 

  8. R. Fagin and J. Y. Halpern. Reasoning about knowledge and probability. Journal of the ACM, 41(2):340–367, 1994.

    Article  Google Scholar 

  9. R. Fagin, J. Y. Halpern, Y. Moses, and M. Y. Vardi. Reasoning about Knowledge. MIT Press, Cambridge, Mass., 1995.

    Google Scholar 

  10. M. J. Fischer and N. Immerman. Foundations of knowledge for distributed systems. In J. Y. Halpern, editor, Theoretical Aspects of Reasoning about Knowledge: Proc. 1986 Conference, pages 171–186. Morgan Kaufmann, San Francisco, Calif., 1986.

    Google Scholar 

  11. G. Gamow and M. Stern. Puzzle Math. Viking Press, New York, 1958.

    Google Scholar 

  12. J. Geanakoplos. Common knowledge. In Y. Moses, editor, Theoretical Aspects of Reasoning about Knowledge: Proc. Fourth Conference, pages 255–315. Morgan Kaufmann, San Francisco, Calif., 1992.

    Google Scholar 

  13. J. Geanakoplos. Common knowledge. In R. Aumann and S. Hart, editors, Handbook of Game Theory, Vol. 2. Elsevier Science, 1994.

    Google Scholar 

  14. J. Gray. Notes on database operating systems. In R. Bayer, R. M. Graham, and G. Seegmuller, editors, Operating Systems: An Advanced Course, Lecture Notes in Computer Science, Vol. 66. Springer-Verlag, Berlin/New York, 1978. Also appears as IBM Research Report RJ 2188, 1978.

    Google Scholar 

  15. J. Y. Halpern and R. Fagin. Modelling knowledge and action in distributed systems. Distributed Computing, 3(4):159–179, 1989. A preliminary version appeared in Proc. 4th ACM Symposium on Principles of Distributed Computing, 1985, with the title “A formal model of knowledge, action, and communication in distributed systems: preliminary report”.

    Article  Google Scholar 

  16. J. Y. Halpern, N. Megiddo, and A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1:170–196, 1985.

    Article  Google Scholar 

  17. J. Y. Halpern and Y. Moses. Knowledge and common knowledge in a distributed environment. Journal of the ACM, 37(3):549–587, 1990. A preliminary version appeared in Proc. 3rd ACM Symposium on Principles of Distributed Computing, 1984.

    Article  Google Scholar 

  18. J. Y. Halpern, Y. Moses, and O. Waarts. A characterization of eventual Byzantine agreement. In Proc. 9th ACM Symp. on Principles of Distributed Computing, pages 333–346, 1990.

    Google Scholar 

  19. J. Y. Halpern and M. R. Tuttle. Knowledge, probability, and adversaries. Journal of the ACM, 40(4):917–962, 1993.

    Article  Google Scholar 

  20. P. Krasucki, R. Parikh, and G. Ndjatou. Probabilistic knowledge and probabilistic common knowledge (preliminary report). In Z. W. Ras, M. Zemankova, and M. L. Emrich, editors, Methodologies for Intelligent Systems, volume 5, pages 1–8. Elsevier Science Publishing Co., Inc., The Hague, 1990.

    Google Scholar 

  21. R. Kurki-Suonio. Towards programming with knowledge expressions. In Proc. 13th ACM Symp. on Principles of Programming Languages, pages 140–149, 1986.

    Google Scholar 

  22. D. Lewis. Convention, A Philosophical Study. Harvard University Press, Cambridge, Mass, 1969.

    Google Scholar 

  23. J. McCarthy, M. Sato, T. Hayashi, and S. Igarishi. On the model theory of knowledge. Technical Report STAN-CS-78-657, Stanford University, 1979.

    Google Scholar 

  24. D. Monderer and D. Samet. Approximating common knowledge with common beliefs. Games and Economic Behavior, 1:170–190, 1989.

    Article  Google Scholar 

  25. S. Morris and H.S. Shin. Approximate common knowledge and co-ordination: Recent lessons from game theory. Journal of Logic, Language and Information, 6:171–190, 1997.

    Article  Google Scholar 

  26. Y. Moses. Knowledge in a distributed environment. PhD thesis, Stanford University, 1986.

    Google Scholar 

  27. Z. Neeman. Approximating agreeing to disagree results with common p-beliefs. Games and Economic Behavior, 12:162–164, 1996.

    Article  Google Scholar 

  28. Z. Neeman. Common beliefs and the existence of speculative trade. Games and Economic Behavior, 16:77–96, 1996.

    Article  Google Scholar 

  29. G. Neiger. Knowledge consistency: a useful suspension of disbelief. In M.Y. Vardi, editor, Proc. Second Conference on Theoretical Aspects of Reasoning about Knowledge, pages 295–308. Morgan Kaufmann, San Francisco, Calif., 1988.

    Google Scholar 

  30. G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334–367, 1993.

    Article  Google Scholar 

  31. P. Panangaden and S. Taylor. Concurrent common knowledge: defining agreement for asynchronous systems. Distributed Computing, 6(2):73–93, 1992.

    Article  Google Scholar 

  32. R. Parikh and R. Ramanujam. Distributed processing and the logic of knowledge. In R. Parikh, editor, Proc. Workshop on Logics of Programs, pages 256–268, 1985.

    Google Scholar 

  33. S. J. Rosenschein. Formal theories of AI in knowledge and robotics. New Generation Computing, 3:345–357, 1985.

    Article  Google Scholar 

  34. S. J. Rosenschein and L. P. Kaelbling. The synthesis of digital machines with provable epistemic properties. In J. Y. Halpern, editor, Theoretical Aspects of Reasoning about Knowledge: Proc. 1986 Conference, pages 83–97. Morgan Kaufmann, San Francisco, Calif., 1986.

    Google Scholar 

  35. A. Rubinstein. The electronic mail game: strategic behavior under “almost common knowledge”. American Economic Review, 79:385–391, 1989.

    Google Scholar 

  36. Y. Yemini and D. Cohen. Some issues in distributed processes communication. In Proc. of the 1st International Conf. on Distributed Computing Systems, pages 199–203, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM Almaden Research Center, 650 Harry Road, San Jose, CA, 95120-6099, USA

    R. Fagin

  2. Department of Computer Science, Cornell University, 14853, Ithaca, NY, USA

    J. Y. Halpern

  3. Department of Electrical Engineering, Technion, 32 000, Haifa, Israel

    Y. Moses

  4. Department of Computer Science, Rice University, Houston, TX, 77005-1892, USA

    M. Y. Vardi

Authors
  1. R. Fagin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Y. Halpern
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Moses
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Y. Vardi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Roskilde University, Denmark

    Vincent F. Hendricks , Klaus Frovin Jørgensen  & Stig Andur Pedersen ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y. (2003). Common Knowledge Revisited. In: Hendricks, V.F., Jørgensen, K.F., Pedersen, S.A. (eds) Knowledge Contributors. Synthese Library, vol 322. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1001-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-1001-6_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1748-3

  • Online ISBN: 978-94-007-1001-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation