Abstract
Revising a belief set K with a proposition a results in a theory that entails a. We consider the case of a multiset of beliefs, representing the beliefs of multiple agents, and define its revision with a multiset of desired beliefs the group of agents should have. We give graph theoretic semantics to this revision operation and we postulate two classes of distance-based revision operators. Further, we show that this multiset revision operation can express the merging of the beliefs of multiple agents.
Support for this project was provided by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and The City University of New York.
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References
Bell, J.L.: A new approach to quantum logic. Br. J. Philos. Sci. 37, 83–99 (1986)
Blizard, W.D., et al.: Multiset theory. Notre Dame J. Formal Logic 30(1), 36–66 (1988)
Deza, M.M., Deza, E.: Encyclopedia of Distances, pp. 1–583. Springer, Heidelberg (2009). doi:10.1007/978-3-642-00234-2
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press, Cambridge (1995)
Georgatos, K.: On indistinguishability and prototypes. Logic J. IGPL 11(5), 531–545 (2003)
Georgatos, K.: Belief update using graphs. In: Proceedings of the Twenty-First International Florida Artificial Intelligence Research Society Conference, pp. 649–654. AAAI Press (2008)
Georgatos, K.: Geodesic revision. J. Logic Comput. 19(3), 447–459 (2009)
Georgatos, K.: Conditioning by minimizing accessibility. In: Bonanno, G., Löwe, B., Hoek, W. (eds.) LOFT 2008. LNCS (LNAI), vol. 6006, pp. 20–33. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15164-4_2
Georgatos, K.: Iterated contraction based on indistinguishability. In: Artemov, S., Nerode, A. (eds.) LFCS 2013. LNCS, vol. 7734, pp. 194–205. Springer, Heidelberg (2013). doi:10.1007/978-3-642-35722-0_14
Georgatos, K.: Graph-based belief merging. In: Hoek, W., Holliday, W.H., Wang, W. (eds.) LORI 2015. LNCS, vol. 9394, pp. 102–115. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48561-3_9
Konieczny, S., Lang, J., Marquis, P.: DA2 merging operators. Artif. Intell. 157(12), 49–79 (2004)
Konieczny, S., Pérez, R.P.: Merging with integrity constraints. In: Hunter, A., Parsons, S. (eds.) ECSQARU 1999. LNCS (LNAI), vol. 1638, pp. 233–244. Springer, Heidelberg (1999). doi:10.1007/3-540-48747-6_22
Lehmann, D.J., Magidor, M., Schlechta, K.: Distance semantics for belief revision. J. Symb. Log. 66(1), 295–317 (2001)
Liberatore, P., Schaerf, M.: Arbitration (or how to merge knowledge bases). IEEE Trans. Knowl. Data Eng. 10(1), 76–90 (1998)
Poincaré, H.: La Valeur de la Science. Flammarion, Paris (1905)
Revesz, P.Z.: On the semantics of theory change: arbitration between old and new information. In: Proceedings of the Twelfth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases, pp. 71–82 (1993)
Schlechta, K.: Non-prioritized belief revision based on distances between models. Theoria 63(1–2), 34–53 (1997)
Zeeman, E.C.: The topology of the brain and visual perception. In: Fort, M.K. (ed.) The Topology of 3-Manifolds, pp. 240–256. Prentice Hall, Englewood Cliffs (1962)
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Georgatos, K. (2017). Multi-agent Belief Revision Using Multisets. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_32
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DOI: https://doi.org/10.1007/978-3-662-55665-8_32
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