Abstract
This paper proposes syntactic combination rules for merging uncertain propositional knowledge bases provided by different sources of information, in the framework of possibilistic logic. These rules are the counterparts of combination rules which can be applied to the possibility distributions (defined on the set of possible worlds), which represent the semantics of each propositional knowledge base. Combination modes taking into account the levels of conflict, the relative reliability of the sources, or having reinforcement effects are considered.
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References
Abidi M.A., Gonzalez R.C. (eds.) (1992) Data Fusion in Robotics and Machine Intelligence. Academic Press, New York.
Baral C., Kraus S., Minker J., Subrahmanian (1992) Combining knowledge bases consisting in first order theories. Computational Intelligence, 8 (1), 45–71.
Benferhat S., Cayrol C., Dubois D., Lang J., Prade H. (1993) Inconsistency management and prioritized syntax-based entailment. Proc. of the 13th Inter. Joint Conf. on Artificial Intelligence (IJCAI’93), Chambéry, France, Aug. 28-Sept. 3, 640–645.
Benferhat S., Dubois D., Prade H. (1995) How to infer from inconsistent beliefs without revising?. Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence (IJCAI’95), Montréal, Canada, Aug. 20–25, 1449–1455.
Boldrin L. (1995) A substructural connective for possibilistic logic In: Symbolic and Quantitative Approaches to Reasoning and Uncertainty (Proc. of Europ. Conf. ECSQARU’95) C. Froidevaux, J. Kohlas, eds.), Springer Verlag, Fribourg, 60–68.
Boldrin L., Sossai C. (1995) An algebraic semantics for possibilistic logic. Proc of the 11th Conf. Uncertainty in Artifucial Intelligence (P. Besnard, S. Hank, eds.) Morgan Kaufmann, San Francisco, CA, 27–35.
Cholvy F. (1992) A logical approach to multi-sources reasoning. In: Applied Logic Conference: Logic at Work, Amsterdam.
Dubois D., Lang J., Prade H. (1987) Theorem proving under uncertainty — A possibility theory-based approach. Proc. of the 10th Inter. Joint Conf. on Artificial Intelligence, Milano, Italy, August, 984–986.
Dubois D., Lang J., Prade H. (1992) Dealing with multi-source information in possibilistic logic. Proc. of the 10th Europ. Conf. on Artificial Intelligence (ECAI’92) Vienna, Austria, Aug. 3–7, 38–42.
Dubois D., Lang J., Prade H. (1994a) Automated reasoning using possibilistic logic: Semantics, belief revision and variable certainty weights. IEEE Trans. on Knowledge and Data Engineering, 6 (1), 64–71.
Dubois D., Lang J., Prade H. (1994b) Possibilistic logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming — Vol 3: Nonmonotonic Reasoning and Uncertain Reasoning (Dov M. Gabbay, C.J. Hogger, J.A. Robinson, D. Nute eds.), Oxford Univ. Press, 439–513.
Dubois D., Prade H. (1988a) Possibility Theory — An Approach to Computerized Processing of Uncertainty. Plenum Press, New York.
Dubois D., Prade H. (1988b) Representation and combination of uncertainty with belief functions and possibility. Computational Intelligence, 4, 244–264.
Dubois D., Prade H. (1988e) Default reasoning and possibility theory. Artificial Intelligence, 35, 243–257.
Dubois D., Prade H. (1988d) On the combination of uncertain or imprecise pieces of information in rule-based systems. A discussion in a framework of possibility theory. Int. Journal of Approximate Reasoning, 2, 65–87.
Dubois D., Prade H. (1990) Aggregation of possibility measures. In: Multiperson Decision Making Using Fuzzy Sets and Possibility Theory (J. Kacprzyk, M. Fedrizzi, eds. ), Kluwer Academic Publ., 55–63.
Dubois D., Prade H. (1992) Combination of fuzzy information in the framework of possibility theory. In: Data Fusion in Robotics and Machine Intelligence ( M.A. Abidi, R.C. Gonzalez, eds.) Academic Press, New York, 481–505.
Dubois D., Prade H. (1994) Possibility theory and data fusion in poorly informed environments. Control Engineering Practice, 2 (5), 811–823.
Dubois D., Prade H. (1996) Belief revision with uncertain inputs in the possibilistic setting. Proc. of the 12th Conf. on Uncertainty in Artificial Intelligence (E. Horvitz, F. Jensen, eds.), Portland, Oregon, Aug. 1–4, 1996, 236–243
Flamm J., Luisi T. (Eds.) (1992) Reliability Data and Analysis. Kluwer Academic Publ.
Kelman A. (1996) Modèles flous pour l’agrégation de données et l’aide à la décision. Thèse de Doctorat, Université Paris 6, France.
Matzkevich I., Abramson B. (1992) The topological fusion of Bayes nets. Proc. of the 8th Conf. on Uncertainty in Artificial Intelligence (D. Dubois, M.P. Wellman, B. D’Ambrosio, P. Smets, eds.), Stanford, CA, July 17–19, 191–198.
Matzkevich I., Abramson B. (1993) Some complexity considerations in the combination of belief networks. Proc. of the 9th Conf. on Uncertainty in Artificial Intelligence (D. Heckerman, A. Mamdani, eds.), Washington, DC, July 9–11, 152–158.
Shafer G. (1976) A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton, NJ.
Shoham Y. (1988) Reasoning About Change — Time and Causation from the Standpoint of Artificial Intelligence. The MIT Press, Cambridge, MA.
Williams M.A. (1996) Towards a practical approach to belief revision: Reason-based change. Proc. of the 5th Conf. on Knowledge Representation and Reasoning Principles (KR’96), Cambridge, MA, Nov. 1996.
Yager R.R. (1987) On the Dempster-Shafer framework and new combination rules. Information Sciences, 41, 93–138.
Yager R. R. (1991) Non-monotonic set-theoritic operators. Fuzzy Sets and Systems 42, 173–190.
Zadeh L.A. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.
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Benferhat, S., Dubois, D., Prade, H. (1998). From Semantic to Syntactic Approaches to Information Combination in Possibilistic Logic. In: Bouchon-Meunier, B. (eds) Aggregation and Fusion of Imperfect Information. Studies in Fuzziness and Soft Computing, vol 12. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1889-5_9
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DOI: https://doi.org/10.1007/978-3-7908-1889-5_9
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-662-11073-7
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