Relating Truth, Knowledge and Belief in Epistemic States

  • Costas D. Koutras
  • Yorgos Zikos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6717)


We define and investigate a structure incorporating what is true, what is known and what is believed by a rational agent in models of the S4.2 logic of knowledge. The notion of KB R -structures introduced, provides a fine-grained modal analysis of an agent’s epistemic state, actually one that differentiates knowledge from belief and accounts for an agent without full introspective power (concerning her knowledge sets). Many epistemic properties of this structure are proved and it is shown that belief collapses in the form of a Stalnaker stable set (while knowledge does not). Finally, a representation theorem is proved, which exactly matches KB R -structures to S4.2 models of the world.


Knowledge Representation modal epistemic logic epistemic states 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    van Benthem, J.: Modal Logic for Open Minds. CSLI Publications, Stanford (2010)Google Scholar
  2. 2.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chellas, B.F.: Modal Logic, an Introduction. Cambridge University Press, Cambridge (1980)CrossRefzbMATHGoogle Scholar
  4. 4.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Heidelberg (2007)CrossRefzbMATHGoogle Scholar
  5. 5.
    Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about Knowledge. MIT Press, Cambridge (2003)zbMATHGoogle Scholar
  6. 6.
    Gabbay, D.M., Woods, J. (eds.): Logic and the Modalities in the Twentieth Century. Handbook of the History of Logic, vol. 7. North-Holland, Amsterdam (2006)zbMATHGoogle Scholar
  7. 7.
    Gochet, P., Gribomont, P.: Epistemic logic. In: Gabbay, Woods (eds.) [6], vol. 7, pp. 99–195 (2006)Google Scholar
  8. 8.
    Goldblatt, R.: Logics of Time and Computation, 2nd edn. CSLI Lecture Notes, vol. 7. Center for the Study of Language and Information, Stanford University (1992)Google Scholar
  9. 9.
    Halpern, J.: A theory of knowledge and ignorance for many agents. Journal of Logic and Computation 7(1), 79–108 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hintikka, J.: Knowledge and Belief: an Introduction to the Logic of the two notions. Cornell University Press, Ithaca (1962)Google Scholar
  11. 11.
    Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge, New York (1996)CrossRefzbMATHGoogle Scholar
  12. 12.
    Janhunen, T., Niemelä, I. (eds.): JELIA 2010. LNCS, vol. 6341. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  13. 13.
    Koutras, C., Zikos, Y.: Relating Truth, Knowledge and Belief in epistemic states. Technical Report, draft version, available through the authors’ web pages, in particular (January 2011),
  14. 14.
    Koutras, C.D., Zikos, Y.: Stable belief sets revisited. In: Janhunen, Niemelä (eds.) [12], pp. 221–233Google Scholar
  15. 15.
    Lenzen, W.: Epistemologische Betrachtungen zu [S4,S5]. Erkenntnis 14, 33–56 (1979)CrossRefGoogle Scholar
  16. 16.
    Marek, V.W., Truszczyński, M.: Non-Monotonic Logic: Context-dependent Reasoning. Springer, Heidelberg (1993)zbMATHGoogle Scholar
  17. 17.
    Segerberg, K.: An essay in Clasical Modal Logic. Filosofiska Studies, Uppsala (1971)zbMATHGoogle Scholar
  18. 18.
    Stalnaker, R.: A note on non-monotonic modal logic. Artificial Intelligence 64, 183–196 (1993); Revised version of the unpublished note originally circulated in 1980MathSciNetCrossRefGoogle Scholar
  19. 19.
    Wooldridge, M.: An Introduction to Multi Agent Systems. John Wiley & Sons, Chichester (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Costas D. Koutras
    • 1
  • Yorgos Zikos
    • 2
  1. 1.Department of Computer Science and TechnologyUniversity of PeloponneseTripolisGreece
  2. 2.Graduate Programme in Logic, Algorithms and Computation (MPLA), Department of MathematicsUniversity of AthensIlissiaGreece

Personalised recommendations