Epistemic Profiles and Belief Structures

  • Barbara Dunin-Kęplicz
  • Andrzej Szałas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7327)

Abstract

The paper is devoted to a novel formalization of beliefs in multiagent systems. Our aim is to bridge the gap between idealized logical approaches to modeling beliefs and their actual implementations. Therefore the stages of belief acquisition, intermediate reasoning and final belief formation are isolated and analyzed. We give a novel semantics reflecting those stages and suitable for building complex belief structures in the context of incomplete and/or inconsistent information. Namely, an agent starts with constituents, i.e., sets of initial beliefs acquired by perception, expert supplied knowledge, communication with other agents and perhaps other ways. Next, the constituents are transformed into consequents according to agents’ epistemic profiles.

Additionally, a uniform treatment of single agent and group beliefs is achieved. Importantly, we indicate an implementation framework ensuring tractability of reasoning about beliefs.

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References

  1. 1.
    Ågotnes, T., Alechina, N.: Full and relative awareness: A decidable logic for reasoning about knowledge of unawareness. In: Proc. of TARK, pp. 6–14. ACM Press (2007)Google Scholar
  2. 2.
    Belnap, N.: A useful four-valued logic. In: Eptein, G., Dunn, J. (eds.) Modern Uses of Many Valued Logic, pp. 8–37. Reidel (1977)Google Scholar
  3. 3.
    Béziau, J.-Y., Carnielli, W., Gabbay, D. (eds.): Handbook of Paraconsistency. College Publications (2007)Google Scholar
  4. 4.
    de Amo, S., Pais, M.: A paraconsistent logic approach for querying inconsistent databases. International Journal of Approximate Reasoning 46, 366–386 (2007)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Dubois, D.: On ignorance and contradiction considered as truth-values. Logic Journal of the IGPL 16(2), 195–216 (2008)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Dunin-Kęplicz, B., Szałas, A.: Implementing belief structures and epistemic profiles: A case study (submitted 2012)Google Scholar
  7. 7.
    Dunin-Kęplicz, B., Verbrugge, R.: Teamwork in Multi-Agent Systems. A Formal Approach. John Wiley & Sons, Ltd. (2010)Google Scholar
  8. 8.
    Dunin-Kęplicz, B., Verbrugge, R.: Awareness as a vital ingredient of teamwork. In: Stone, P., Weiss, G. (eds.) Proc. of AAMAS 2006, pp. 1017–1024 (2006)Google Scholar
  9. 9.
    Fagin, R., Halpern, J.: Belief, awareness, and limited reasoning. Artificial Intelligence 34(1), 39–76 (1988)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning About Knowledge. The MIT Press (2003)Google Scholar
  11. 11.
    Gottlob, G.: Complexity results for nonmonotonic logics. Journal of Logic and Computation 2(3), 397–425 (1992)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Hintikka, J.: Knowledge and Belief. Cornell University Press (1962)Google Scholar
  13. 13.
    Kraus, S., Lehmann, D.: Knowledge, belief, and time. Theoretical Computer Science 58, 155–174 (1988)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Laux, A., Wansing, H. (eds.): Knowledge and Belief in Philosophy and Artificial Intelligence. Akademie Verlag, Berlin (1995)MATHGoogle Scholar
  15. 15.
    Łukaszewicz, W.: Non-Monotonic Reasoning - Formalization of Commonsense Reasoning. Ellis Horwood (1990)Google Scholar
  16. 16.
    Małuszyński, J., Szałas, A.: Living with Inconsistency and Taming Nonmonotonicity. In: de Moor, O., Gottlob, G., Furche, T., Sellers, A. (eds.) Datalog 2010. LNCS, vol. 6702, pp. 384–398. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    Małuszyński, J., Szałas, A.: Logical foundations and complexity of 4QL, a query language with unrestricted negation. Journal of Applied Non-Classical Logics 21(2), 211–232 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Marek, V., Truszczyński, M.: Nonmonotonic Logic. Springer (1993)Google Scholar
  19. 19.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer (2007)Google Scholar
  20. 20.
    Vitória, A., Małuszyński, J., Szałas, A.: Modeling and reasoning with paraconsistent rough sets. Fundamenta Informaticae 97(4), 405–438 (2009)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Barbara Dunin-Kęplicz
    • 1
    • 2
  • Andrzej Szałas
    • 1
    • 3
  1. 1.Institute of InformaticsUniversity of WarsawPoland
  2. 2.Institute of Computer SciencePolish Academy of SciencesWarsawPoland
  3. 3.Department of Computer and Information ScienceLinköping UniversitySweden

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