Advertisement

Distributed Knowledge with Justifications

  • Meghdad Ghari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7415)

Abstract

In this paper, we introduce justification counterparts of distributed knowledge logics. Our justification logics include explicit knowledge operators of the form [[t]] iF and \([[t]]_{\mathcal D} F\), which are interpreted respectively as “t is a justification that agent i accepts for F”, and “t is a justification that all agents implicitly accept for F”. We present Kripke style models and prove the completeness theorem. Finally, we give a semantical proof of the realization theorem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Artemov, S.: Explicit provability and constructive semantics. Bulletin of Symbolic Logic 7(1), 1–36 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Artemov, S.: The logic of justification. The Review of Symbolic Logic 1(4), 477–513 (2008)zbMATHCrossRefGoogle Scholar
  3. 3.
    Artemov, S.: Tracking Evidence. In: Blass, A., Dershowitz, N., Reisig, W. (eds.) Fields of Logic and Computation. LNCS, vol. 6300, pp. 61–74. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Bucheli, S., Kuznets, R., Renne, B., Sack, J., Studer, T.: Justified belief change. In: Arrazola, X., Ponte, M. (eds.) Proceedings of the Second ILCLI International Workshop on Logic and Philosophy of Knowledge, Communication and Action, LogKCA 2010, pp. 135–155. University of the Basque Country Press (2010)Google Scholar
  5. 5.
    Bucheli, S., Kuznets, R., Studer, T.: Justifications for common knowledge. Journal of Applied Non-Classical Logics 21(1), 35–60 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bucheli, S., Kuznets, R., Studer, T.: Partial Realization in Dynamic Justification Logic. In: Beklemishev, L.D., de Queiroz, R. (eds.) WoLLIC 2011. LNCS, vol. 6642, pp. 35–51. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Fagin, R., Halpern, J.Y., Vardi, M.Y.: What can machines know? on the properties of knowledge in distributed systems. Journal of the ACM 39, 328–376 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about knowledge. MIT Press (1995)Google Scholar
  9. 9.
    Fitting, M.: The logic of proofs, semantically. Annals of Pure and Applied Logic 132(1), 1–25 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Ghari, M.: Justification counterpart of distributed knowledge systems. In: Slavkovik, M. (ed.) Proceedings of the 15th ESSLLI Student Session, Copenhagen, Denmark, pp. 25–36 (2010)Google Scholar
  11. 11.
    Goetschi, R., Kuznets, R.: Realization for Justification Logics via Nested Sequents: Modularity through Embedding. Annals of Pure and Applied Logic (to appear)Google Scholar
  12. 12.
    Meyer, J.-J.C., van der Hoek, W.: Epistemic logic for AI and computer science. Cambridge University Press (1995)Google Scholar
  13. 13.
    Renne, B.: Public communication in justification logic. Journal of Logic and Computation 21(6), 1005–1034 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Renne, B.: Multi-Agent Justification Logic: Communication and Evidence Elimination. Synthese (Published Online July 5, 2011)Google Scholar
  15. 15.
    Yavorskaya (Sidon), T.: Interacting explicit evidence systems. Theory of Computing Systems 43, 272–293 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Studer, T.: Justification logic, inference tracking, and data privacy. Logic and Logical Philosophy 20(4), 297–306 (2011)MathSciNetGoogle Scholar
  17. 17.
    Studer, T.: An application of justification logic to protocol verification. In: Proceedings of 2011 Seventh International Conference on Computational Intelligence and Security, CIS 2011, pp. 779–783. IEEE (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Meghdad Ghari
    • 1
  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

Personalised recommendations