Abstract
We present tableau calculi for some logics of default reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for preferential and cumulative logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. Moreover, they give a decision procedure for the respective logics and can be used to establish their complexity.
This research has been partially supported by the project MIUR PRIN 2003 ”Logic-based development and verication of multi-agent systems”.
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Artosi, A., Governatori, G., Rotolo, A.: Labelled tableaux for non-monotonic reasoning: Cumulative consequence relations. Journal of Logic and Computation 12(6), 1027–1060 (2002)
Boutilier, C.: Conditional logics of normality: a modal approach. Artificial Intelligence 68(1), 87–154 (1994)
Crocco, G., Lamarre, P.: On the connection between non-monotonic inference systems and conditional logics. In: Proc. of KR 1992, pp. 565–571 (1992)
Friedman, N., Halpern, J.Y.: Plausibility measures and default reasoning. Journal of the ACM 48(4), 648–685 (2001)
Friedman, N., Halpern, J.Y., Koller, D.: First-order conditional logic for default reasoning revisited. ACM TOCL 1(2), 175–207 (2000)
Gabbay, D.: Theoretical foundations for non-monotonic reasoning in expert systems. In: Logics and models of concurrent systems, pp. 439–457. Springer, Heidelberg (1985)
Giordano, L., Gliozzi, V., Olivetti, N., Schwind, C.: Tableau calculi for preference-based conditional logics. In: Cialdea Mayer, M., Pirri, F. (eds.) TABLEAUX 2003. LNCS (LNAI), vol. 2796, pp. 81–101. Springer, Heidelberg (2003)
Goré, R.: Tableau methods for modal and temporal logics. In: Handbook of Tableau Methods, pp. 297–396. Kluwer Academic Publishers, Dordrecht (1999)
Heuerding, A., Seyfried, M., Zimmermann, H.: Efficient loop-check for backward proof search in some non-classical propositional logics. In: Miglioli, P., Moscato, U., Ornaghi, M., Mundici, D. (eds.) TABLEAUX 1996. LNCS (LNAI), vol. 1071, pp. 210–225. Springer, Heidelberg (1996)
Katsuno, H., Sato, K.: A unified view of consequence relation, belief revision and conditional logic. In: Proc. IJCAI 1991, pp. 406–412 (1991)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44(1-2), 167–207 (1990)
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence 55(1), 1–60 (1992)
Shoham, Y.: A semantical approach to nonmonotonic logics. In: Proceedings of Logics in Computer Science, pp. 275–279 (1987)
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Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L. (2005). Analytic Tableaux for KLM Preferential and Cumulative Logics. In: Sutcliffe, G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11591191_46
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DOI: https://doi.org/10.1007/11591191_46
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