Matrix representation of belief states: An algebraic semantics for belief logics

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 12, Issue 5, 2004, Pages 613-633

  Liau, Churn Jung ^a  

^a INSTITUTE OF INFORMATION SCIENCE   (Taiwan)

Author keywords

Belief fusion; Belief reasoning; Belief revision; Belief states; Intelligent agents; Matrix algebra

Indexed keywords

BOOLEAN ALGEBRA; COMPUTATIONAL METHODS; INFORMATION THEORY; INTELLIGENT AGENTS; KNOWLEDGE BASED SYSTEMS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; SEMANTICS;

BELIEF FUSION; BELIEF REASONING; BELIEF REVISION; BELIEF STATES;

MATRIX ALGEBRA;

EID: 10644281149     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218488504003119     Document Type: Article

References (37)

1. C.E. Alchourrón, P. Gärdenfors, and D. Makinson. "On the logic of theory change: Partial meet contraction and revision functions". Journal of Symbolic Logic, 50:510-530, 1985.
2. C. Baral, S. Kraus, J. Minker, and V. S. Subrahmanian. "Combining knowledge bases consisting of first-order theories". Computational Intelligence, 8(1):45-71, 1992.
3. S. Benferhat, D. Dubois, and O. Papini. "A sequential belief revision methods based on polynomials". In Proceedings of the 16th National Conference on Artificial Intelligence, pages 733-738. AAAI Press, 1999.
4. S. Benferhat, D. Dubois, and H. Prade. "Representing default rules in possibilistic logic". In B. Nebel, C. Rich, and W. Swartout, editors, Proceedings of the 3rd International Conference on Principle of Knowledge Representation and Reasoning, pages 673-684. Morgan Kaufmann, 1992.
5. S. Benferhat, D. Dubois, and H. Prade. "From semantic to syntactic approaches to information combination in possibilistic logic". In B. Bouchon-Meunier, editor, Aggregation and Fusion of Imperfect Information, pages 141-161. Physica-Verlag, 1997.
6. C. Boutilier. "Inaccessible worlds and irrelevance: Preliminary report". In Proceedings of the 12th International Joint Conference on Artificial Intelligence, pages 413-418, 1991.
7. C. Boutilier. "A logic for revision and subjunctive queries". In Proceedings of the 10th National Conference on Artificial Intelligence, pages 609-615. MIT Press, 1992.
8. C. Boutilier. "Modal logics for qualitative possibility and beliefs". In D. Dubois et al., editor, Proceedings of the 8th Annual Conference of Uncertainty in Artificial Intelligence, pages 17-24. Morgan Kaufmann, 1992.
9. C. Boutilier. "Revision sequences and nested conditionals". In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pages 519-525, 1993.
10. C. Boutilier. "Generalized update: Belief change in dynamic settings". In Proceedings of the 14th International Joint Conference on Artificial Intelligence, pages 1550-1556, 1995.
11. L. Cholvy. "A logiccal approach to multi-souces reasoning". In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning under Uncertainty, LNCS 808, pages 183-196. Springer-Verlag, 1994.
12. A. Darwiche and J. Pearl. "On the logic of iterated belief revision". Artificial Intelligence, 89(1):1-29, 1997.
13. D. Dubois and H. Prade. "Belief change and possibility theory". In P. Gärdenfors, editor, Belief Revision, pages 142-182. Cambridge University Press, 1992.
14. D. Dubois and H. Prade. "Possibility theory in information fusion". In Proc. of the Third International Conference on Information Fusion, pages TuA-1, 2000.
15. R. Fagin, J.Y. Halpern, Y. Moses, and M.Y. Vardi. Reasoning about Knowledge. MIT Press, 1996.
16. D.M. Gabbay. "Theoretical foundations for nonmonotonic reasoning in expert systems". In K. Apt, editor, Logics and Models of Concurrent Systems, pages 439-459. Springer-Verlag, 1985.
17. J.Y. Halpern and Y. Moses. "A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54:311-379, 1992.
18. P. Maynard-Reid II and D. Lehmann. "Representing and aggregating conflicting beliefs". In Proceedings of the 7th International Conference on Principles of Knowledge Representation and Reasoning, pages 153-164, 2000.
19. P. Maynard-Reid II and Y. Shoham. "Belief fusion: Aggregating pedigreed belief states". Journal of Logic, Language and Information, 10(2): 183-209, 2001.
20. H. Katsuno and A. Medelzon. "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'91), pages 387-394. Morgan Kaufmann Publisher, 1991.
21. H. Katsuno and A. Medelzon. "Prepositional knowledge base revision and minimal change". Artificial Intelligence, 52:263-294, 1991.
22. S. Konieczny. "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'00)., pages 135-144. Morgan Kaufmann Publisher, 2000.
23. S. Kraus, D. Lehmann, and M. Magidor. "Nonmonotonic reasoning, preferential models and cumulative logics". Artificial Intelligence, 44:167-207, 1990.
24. D. Lehmann. "What does a conditional knowledge base entail?". In R. Brachman and H. J. Levesque, editors, Proceedings of the 1st International Conference on Principle of Knowledge Representation and Reasoning, pages 212-222. Morgan Kaufmann, 1989.
25. D. Lehmann. "Belief revision, revised". In Proceedings of the 14th International Joint Conference on Artificial Intelligence, pages 1534-1540, 1995.
26. C. J. Liau. "A conservative approach to distributed belief fusion". In Proc. of the Third International Conference on Information Fusion, pages MoD4-1, 2000.
27. C.J. Liau. "A modal logic framework for multi-agent belief fusion". ACM Transactions on Computational Logic, to appear, 2004.
28. C.J. Liau. "Belief reasoning, revision and fusion by matrix algebra". In S. Tsumoto, R. Slowinski, J. Komorowski, and J. Grzymala-Busse, editors, The 4th International Conference on Rough Sets and Current Trends in Computing (RSCTC 2004), LNAI, to appear. Springer-Verlag, 2004.
29. J. Lin. "Information sharing and knowledge merging in cooperative information systems". In Proceedings of the Fourth Workshop on Information Technologies and Systems, pages 58-66, 1994.
30. J. Lin and A.O. Mendelzon. "Knowledge base merging by majority". In R. Pareschi and B. Fronhoefer, editors, Dynamic Worlds: From the Frame Problem to Knowledge Management. Kluwer Academic Publisher, 1999.
31. W. Lukaszewicz. Nonmonotonic Reasoning: Formalisation of Commonsense Reasoning. Ellis Horwood, New York, 1990.
32. S. Pradhan, J. Minker, and V. Subrahmanian. "Combining databases with prioritized information". Journal of Intelligent Information Systems, 4(3):231-260, 1995.
33. K. Segerberg. "Belief revision from the point of view of doxastic logic". Bulletin of the IGPL, 3(4):535-553, 1995.
34. P. Smets. "Data fusion in the transferable belief model". In Proc. of the Third International Conference on Information Fusion, pages WeA-1, 2000.
35. W. Spohn. "Ordinal conditional functions: a dynamic theory of epistemic states". In W.L. Harper and B. Skyrms, editors, Causation in Decision, Belief Change, and Statistics, II, pages 105-134. Kluwer Academic Publishers, 1988.
36. V.S. Subrahmanian. "Amalgamating knowledge bases". ACM Transactions on Database Systems, 19(2):291-331, 1994.
37. M.A. Williams. "Transmutations of knowledge systems". In J. Doyle, E. Sandewall, and P. Torasso, editors, Proceedings of the 4th International Conference on Principle of Knowledge Representation and Reasoning, pages 619-629. Morgan Kaufmann Publishers, 1994.