Advertisement

Belief Reasoning, Revision and Fusion by Matrix Algebra

  • Churn-Jung Liau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3066)

Abstract

Representation of belief states is an important issue forknowledge based systems. In this paper, we develop a matrix representation for ordered belief states and show that belief reasoning, revision and fusion can all be interpreted as operations of matrix algebra. Thus, the matrix representation can serve as the basis of algebraic semantics for belief logic.

Keywords

Belief states matrix algebra belief reasoning belief revision belief fusion multi-agent systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alchourrón, C.E., Gärdenfors, Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50, 510–530 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Baral, C., Kraus, S., Minker, J., Subrahmanian, V.S.: Combining knowledge bases consisting of first-order theories. Computational Intelligence 8(1), 45–71 (1992)CrossRefGoogle Scholar
  3. 3.
    Benferhat, S., Dubois, D., Prade, H.: From semantic to syntactic approaches to information combination in possibilistic logic. In: Bouchon-Meunier, B. (ed.) Aggregation and Fusion of Imperfect Information, pp. 141–161. Physica-Verlag, Heidelberg (1997)Google Scholar
  4. 4.
    Boutilier, C.: Revision sequences and nested conditionals. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence, pp. 519–525 (1993)Google Scholar
  5. 5.
    Boutilier, C.: Generalized update: Belief change in dynamic settings. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence, pp. 1550–1556 (1995)Google Scholar
  6. 6.
    Cholvy, L.: A logiccal approach to multi-souces reasoning. In: Masuch, M., Polos, L. (eds.) Logic at Work 1992. LNCS, vol. 808, pp. 183–196. Springer, Heidelberg (1994)Google Scholar
  7. 7.
    Darwiche, A., Pearl, J.: On the logic of iterated belief revision. Artificial Intelligence 89(1), 1–29 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Dubois, D., Prade, H.: Belief change and possibility theory. In: Gärdenfors, P. (ed.) Belief Revision, pp. 142–182. Cambridge University Press, Cambridge (1992)CrossRefGoogle Scholar
  9. 9.
    Dubois, D., Prade, H.: Possibility theory in information fusion. In: Proc. of the Third International Conference on Information Fusion, pages TuA–1 (2000)Google Scholar
  10. 10.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1996)Google Scholar
  11. 11.
    Halpern, J.Y., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence 54, 311–379 (1992)MathSciNetGoogle Scholar
  12. 12.
    Maynard-Reid II, P., Lehmann, D.: Representing and aggregating conflicting beliefs. In: Proceedings of the 7th International Conference on Principles of Knowledge Representation and Reasoning, pp. 153–164 (2000)Google Scholar
  13. 13.
    Maynard-Reid II, P., Shoham, Y.: Belief fusion: Aggregating pedigreed belief states. Journal of Logic, Language and Information 10(2), 183–209 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Katsuno, H., Medelzon, A.: On the difference between updating a knowledge base and revising it. In: Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR 1991), pp. 387–394. Morgan Kaufmann Publisher, San Francisco (1991)Google Scholar
  15. 15.
    Katsuno, H., Medelzon, A.: Propositional knowledge base revision and minimal change. Artificial Intelligence 52, 263–294 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Konieczny, S.: On the difference between merging knowledge bases and combining them. In: Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2000), pp. 135–144. Morgan Kaufmann Publisher, San Francisco (2000)Google Scholar
  17. 17.
    Lehmann, D.: Belief revision, revised. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence, pp. 1534–1540 (1995)Google Scholar
  18. 18.
    Liau, C.J.: A conservative approach to distributed belief fusion. In: Proc. of the Third International Conference on Information Fusion, pages MoD4–1 (2000)Google Scholar
  19. 19.
    Liau, C.J.: Epistemic logics for information fusion. In: Nielsen, T.D., Zhang, N.L. (eds.) ECSQARU 2003. LNCS (LNAI), vol. 2711, pp. 489–501. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. 20.
    Liau, C.J.: A modal logic framework for multi-agent belief fusion. ACM Transactions on Computational Logic (2004)Google Scholar
  21. 21.
    Lin, J.: Information sharing and knowledge merging in cooperative information systems. In: Proceedings of the Fourth Workshop on Information Technologies and Systems, pp. 58–66 (1994)Google Scholar
  22. 22.
    Lin, J., Mendelzon, A.O.: Knowledge base merging by majority. In: Pareschi, R., Fronhoefer, B. (eds.) Dynamic Worlds: From the Frame Problem to Knowledge Management, Kluwer Academic Publisher, Dordrecht (1999)Google Scholar
  23. 23.
    Pradhan, S., Minker, J., Subrahmanian, V.: Combining databases with prioritized information. Journal of Intelligent Information Systems 4(3), 231–260 (1995)CrossRefGoogle Scholar
  24. 24.
    Segerberg, K.: Belief revision from the point of view of doxastic logic. Bull. of the IGPL 3(4), 535–553 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Smets, P.: Data fusion in the transferable belief model. In: Proc. of the Third International Conference on Information Fusion, pages WeA–1 (2000)Google Scholar
  26. 26.
    Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper, W.L., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics, II, pp. 105–134. Kluwer Academic Publishers, Dordrecht (1988)Google Scholar
  27. 27.
    Subrahmanian, V.S.: Amalgamating knowledge bases. ACM Transactions on Database Systems 19(2), 291–331 (1994)CrossRefMathSciNetGoogle Scholar
  28. 28.
    Williams, M.A.: Transmutations of knowledge systems. In: Doyle, J., Sandewall, E., Torasso, P. (eds.) Proceedings of the 4th International Conference on Principle of Knowledge Representation and Reasoning, pp. 619–629. Morgan Kaufmann Publishers, San Francisco (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Churn-Jung Liau
    • 1
  1. 1.Institute of Information ScienceAcademia SinicaTaipeiTaiwan

Personalised recommendations