On the Interactions of Awareness and Certainty

  • Hans van Ditmarsch
  • Tim French
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7106)

Abstract

We examine the interactions of knowledge and awareness in dynamic epistemic logic. Implicit knowledge describes the things that an agent could infer from what is known, if the agent were aware of the necessary concepts. Reasoning techniques that are robust to incomplete awareness are important when considering interactions of automated agents in complex dynamic environments, such as the semantic web. Here we revisit Hector Levesque’s original motivation of implicit knowledge and consider several contemporary realizations of implicit knowledge. We present a framework to compare different interactions of knowledge and awareness in the context of public announcements, and introduce a new formalism for tacit knowledge.

Keywords

Modal Logic Tacit Knowledge Explicit Knowledge Implicit Knowledge Epistemic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Agotnes, T., Alechina, N.: Full and relative awareness: a decidable logic for reasoning about knowledge of unawareness. In: Proceedings of TARK XI, pp. 6–14. ACM, New York (2007)Google Scholar
  2. 2.
    van Benthem, J., Velazquez-Quesada, F.: Inference, promotion and the dynamics of awareness. In: Knowledge, Rationality and Action (2009)Google Scholar
  3. 3.
    Cadoli, M., Schaerf, M.: Approximate reasoning and non-omniscient agents. In: TARK (1992)Google Scholar
  4. 4.
    van Ditmarsch, H., French, T.: Becoming Aware of Propositional Variables. In: Banerjee, M., Seth, A. (eds.) Logic and Its Applications. LNCS, vol. 6521, pp. 204–218. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic, Synthese Library, vol. 337. Springer, Heidelberg (2007)CrossRefMATHGoogle Scholar
  6. 6.
    Fagin, R., Halpern, J.: Belief, awareness, and limited reasoning. Artificial Intelligence 34(1), 39–76 (1988)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about Knowledge. MIT Press, Cambridge (1995)MATHGoogle Scholar
  8. 8.
    Grossi, D., Velázquez-Quesada, F.R.: Twelve Angry Men: A Study on the Fine-Grain of Announcements. In: He, X., Horty, J., Pacuit, E. (eds.) LORI 2009. LNCS, vol. 5834, pp. 147–160. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Halpern, J., Rego, L.: Reasoning about knowledge of unawareness. Games and Economic Behavior 67(2), 503–525 (2009)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Heifetz, A., Meier, M., Schipper, B.: Interactive unawareness. Journal of Economic Theory 130, 78–94 (2006)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Hill, B.: Awareness dynamics. Journal of Philosophical Logic 39, 113–137 (2010)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Sim, K.M.: Epistemic logic and logical omniscience ii: A unifying framework. International Journal of Intelligent Systems 15 (2000)Google Scholar
  13. 13.
    Levesque, H.: Logic of implicit and explicit belief. In: Proceedings of AAAI 1984, pp. 198–202 (1984)Google Scholar
  14. 14.
    Modica, S., Rustichini, A.: Unawareness and partitional information structures. Games and Economic Behavior 27, 265–298 (1999)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Polanyi, M.: The logic of tacit inference. Philosophy 41, 1 (1966)CrossRefGoogle Scholar
  16. 16.
    Sillari, G.: Quantified logic of awareness and impossible possible worlds. Review of Symbolic Logic 1(4), 514–529 (2008)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Velázquez-Quesada, F.R.: Inference and update. Synthese (Knowledge, Rationality and Action) 169(2), 283–300 (2009)MathSciNetMATHGoogle Scholar
  18. 18.
    Velazquez-Quesada, F.: Small steps in dynamics of information. Ph.D. thesis, University of Amsterdam (2011), iLLC Dissertation Series DS-2011-02Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hans van Ditmarsch
    • 1
    • 2
  • Tim French
    • 3
  1. 1.Department of LogicUniversity of SevillaSpain
  2. 2.Institute of Mathematical SciencesChennaiIndia
  3. 3.Computer Science and Software EngineeringThe University of Western AustraliaAustralia

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