Journal of Logic, Language and Information

, Volume 10, Issue 2, pp 183–209 | Cite as

Belief Fusion: Aggregating Pedigreed Belief States

  • Pedrito Maynard-ReidII
  • Yoav Shoham

Abstract

We introduce a new operator – belief fusion– which aggregates the beliefs of two agents, each informed by a subset of sources ranked by reliability. In the process we definepedigreed belief states, which enrich standard belief states with the source of each piece of information. We note that the fusion operator satisfies the invariants of idempotence, associativity, and commutativity. As a result, it can be iterated without difficulty. We also define belief diffusion; whereas fusion generally produces a belief state with more information than is possessed by either of its two arguments, diffusion produces a state with less information. Fusion and diffusion are symmetric operators, and together define a distributive lattice. Finally, we show that AGM revision can be viewed as fusion between a novice and an expert.

belief aggregation knowledge representation multi-agent systems 

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References

  1. Alchourrón, C.E., Gärdenfors, P., and Makinson, D., 1985, “On the logic of theory change: Partial meet contraction and revision functions,” Journal of Symbolic Logic 50, 510–530.CrossRefGoogle Scholar
  2. Arrow, K.J., 1963, Social Choice and Individual Values, 2nd edition, New York: Wiley.Google Scholar
  3. Baral, C., Kraus, S., Minker, J., and Subrahmanian, V.S., 1992, “Combining knowledge bases consisting of first-order theories,” Computational Intelligence 8, 45–71.Google Scholar
  4. Benferhat, S., Dubois, D., and Prade, H., 1997, “From semantic to syntactic approaches to information combination in possibilistic logic,” pp. 141–161 in Aggregation and Fusion of Imperfect Information, Studies in Fuzziness and Soft Computing, B. Bouchon-Meunier, ed., New York: Physica Verlag.Google Scholar
  5. Birkhoff, G., 1948, Lattice Theory, Colloquium Publications, Vol. 25, Providence, RI: American Mathematical Society.Google Scholar
  6. Borgida, A. and Imielinski, T., 1984, “Decision making in committees: A framework for dealing with inconsistency and non-monotonicity,” pp. 21–32 in Proceedings of the Workshop on Nonmonotonic Reasoning, New Paltz, NY.Google Scholar
  7. Boutilier, C., 1996, “Iterated revision and minimal change of conditional beliefs,” Journal of Philosophical Logic 25, 263–305.CrossRefGoogle Scholar
  8. Boutilier, C. and Goldszmidt, M., 1995, “On the revision of conditional belief sets,” pp. 267–300 in Conditionals: From Philosophy to Computer Science, G. Crocco, L. Fariñas del Cerro, and A. Herzig, eds., Oxford: Oxford University Press.Google Scholar
  9. Cantwell, J., 1998, “Resolving conflicting information,” Journal of Logic, Language, and Information 7, 191–220.CrossRefGoogle Scholar
  10. Darwiche, A. and Pearl, J., 1997, “On the logic of iterated belief revision,” Artificial Intelligence 89, 1–29.CrossRefGoogle Scholar
  11. Freund, M. and Lehmann, D., 1994, “Belief revision and rational inference,” Technical Report TR 94–16, Hebrew University.Google Scholar
  12. Friedman, N. and Halpern, J.Y., 1996, “Belief revision: A critique,” pp. 421–431 in Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning (KR '96), L. Aiello, J. Doyle, and S. Shapiro, eds., San Francisco, CA: Morgan Kaufmann.Google Scholar
  13. Gärdenfors, P., 1988, Knowledge in Flux: Modeling the Dynamics of Epistemic States, Cambridge, MA: MIT Press.Google Scholar
  14. Grove, A., 1988, “Two modellings for theory change,” Journal of Philosophical Logic 17, 157–170.CrossRefGoogle Scholar
  15. Hansson, S.-O., ed., 1997, Theoria: A Swedish Journal of Philosophy, Special Issue on Non-Prioritized Belief Revision, 63(1–2).Google Scholar
  16. Jeffrey, R.C., 1965, The Logic of Decision, Chicago: University Press.Google Scholar
  17. Katsuno, H. and Mendelzon, A.O., 1991, “Propositional knowledge base revision and minimal change,” Artificial Intelligence 52, 263–294.CrossRefGoogle Scholar
  18. Konieczny, S. and Pérez, R.P., 1998, “On the logic of merging,” pp. 488–498 in Proceedings of the Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR '98), A. Cohn, L. Shubert, and S. Shapiro, eds., San Francisco, CA: Morgan Kaufmann.Google Scholar
  19. Lehmann, D., 1995, “Belief revision, revised,” pp. 1534–1540 in Proceedings of the Fourteenth International Joint Conference of Artificial Intelligence (IJCAI '95), S. Mellish, ed., San Mateo, CA: Morgan Kaufmann.Google Scholar
  20. Liberatore, P. and Schaerf, M., 1995, “Arbitration: A commutative operator for belief revision,” pp. 217–228 in Proceedings of the Second World Conference on the Fundamentals of Artificial Intelligence (WOCFAI '95), M. De Glas and Z. Pawlak, eds., Paris, France.Google Scholar
  21. Maynard-Reid II, P. and Lehmann, D., 2000, “Representing and aggregating conflicting beliefs,” pp. 153–164 in Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning (KR2000), A.G. Cohn, F. Giunchiglia, and B. Selman, eds., San Francisco, CA: Morgan Kaufmann.Google Scholar
  22. Maynard-Reid II, P. and Shoham, Y., 1998, “From belief revision to belief fusion,” in Proceedings of the Third Conference on Logic and the Foundations of Game and Decision Theory (LOFT3), Torino, Italy: ICER.Google Scholar
  23. Nayak, A.C., 1994, “Iterated belief change based on epistemic dntrenchment,” Erkenntnis 41, 353–390.CrossRefGoogle Scholar
  24. Nayak, A.C., Foo, N.Y., Pagnucco, M., and Sattar, A., 1996, “Changing conditional beliefs unconditionally,” pp. 119–135 in Proceedings of the Sixth Conference on Theoretical Aspects of Rationality and Knowledge (TARK VI), Y. Shoham, ed., The Netherlands: De Zeeuwse Stromen.Google Scholar
  25. Revesz, P.Z., 1993, “On the semantics of theory change: Arbitration between old and new information,” pp. 71–82 in Proceedings of the Twelfth ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS '93), New York: ACM Press.CrossRefGoogle Scholar
  26. Sen, A., 1986, “Social choice theory,” pp. 1073–1181 in Handbook of Mathematical Economics, Vol. III, K.J. Arrow and M.D. Intriligator, eds., Amsterdam: Elsevier Science Publishers.Google Scholar
  27. Spohn, W., 1988, “Ordinal conditional functions: A dynamic theory of epistemic states,” pp. 105–134 in Causation in Decision, Belief Change, and Statistics, II, W.L. Harper and B. Skyrms, eds., Dordrecht: Kluwer Academic Publishers.Google Scholar
  28. Williams, M.-A., 1994, “Transmutations of knowledge systems,” pp. 619–629 in Proceedings of the Fourth International Conference on Principles of Knowledge Representation and Reasoning (KR '94), J. Doyle, E. Sandewall, and P. Torasso, eds., San Francisco, CA: Morgan Kaufmann.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Pedrito Maynard-ReidII
    • 1
  • Yoav Shoham
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanfordU.S.A.

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