Abstract
Reiter’s default logic can not handle inconsistencies and incoherences and thus is not satisfactory enough in commonsense reasoning. In the paper we propose a new variant of default logic named FDL in which the existence of extension is guaranteed and the trivial extension is avoided. Moreover, Reiter’s default extensions are reserved and can be identified from the other extensions in FDL. Technically, we develop a paraconsistent and monotonic reasoning system based on resolution as the underlying logic of FDL. The definition of extension is also modified in the manner that conflicts between justifications of the used defaults and the conclusions of the extension, which we call justification conflicts, are permitted, so that justifications can not be denied by “subsequent” defaults and the existence of extension is guaranteed. Then we select the desired extensions as preferred ones according to the criteria that justification conflicts should be minimal.
This work is partially supported by NSFC (grant number 60373002 and 60496322) and NKBRPC (grant number 2004CB318000).
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References
Reiter, R.: A logic for default reasoning. Artificial Intelligence 13, 81–132 (1980)
Papadimitriou, C.H., Sideri, M.: Default theories that always have extensions. Artificial Intelligence 69(1-2), 347–357 (1994)
Cholewinski, P.: Reasoning with stratified default theories. Logic Programming and Nonmonotonic Reasoning 928, 273–286 (1995)
Linke, T., Schaub, T.: Alternative foundations for Reiter’s default logic. Artificial Intelligence 124(1), 31–86 (2000)
daCosta, N.: Theory of inconsistent formal systems. Notre Dame Journal of Formal Logic 15, 497–510 (1974)
Lin, Z., Li, W.: On logic of paradox. In: Proceedings of the 25th IEEE International Symposium on Multipl-Valued Logic, pp. 248–255 (1995)
Lin, Z.: Paraconsistent circumscription. Journal of Pattern Recognition and Artificial Intelligence 10(6), 679–686
Besnard, P., Schaub, T.: Signed system for paraconsistent reasoning. Journal of Automated Reasoning 20(1-2), 191–213 (1998)
Belnap, N.: How computer should think. In: Contemporary Aspects of Philosophy, pp. 7–37 (1977)
Belnap, N.: A useful four-valued logic. In: Modern uses of multiple-valued logic, pp. 30–56 (1977)
Arieli, O., Avron, A.: The value of the four values. Artificial Intelligence 102(1), 97–141 (1998)
Ginsberg, M.L.: Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, 265–316 (1988)
Han, Q., Lin, Z.: Paraconsistent default reasoning. In: 10th International Workshop on Non-Monotonic Reasoning, pp. 197–203 (2004)
Yue, A., Lin, Z.: Default logic based on four valued semantics. Chinese journal of computer 28(9), 1447–1458 (2005)
Lukaszewicz, W.: Considerations on default logic: an alternative approach. Computational Intelligence 4(1), 1–16 (1988)
Schaub, T.: On constrained default theories. In: ECAI, pp. 304–308 (1992)
Brewka, G.: Cumulative default logic: in defense of nonmonotonic inference rules. Artificial Intelligence 50(2), 183–205 (1991)
Shoham, Y.: A semantical approach to nonmonotonic logics. In: Ginsberg, M.L. (ed.) Readings in Nonmonotonic Reasoning, pp. 227–250. Kaufmann, Los Altos (1987)
Shoham, Y.: Reasoning about change: time and causation from the standpoint of artificial intelligence. MIT Press, Cambridge (1988)
Lehmann, D.J.: Plausibility logic. In: Kleine Büning, H., Jäger, G., Börger, E., Richter, M.M. (eds.) CSL 1991. LNCS, vol. 626, pp. 227–241. Springer, Heidelberg (1992)
Marek, W., Truszczyński, M.: Nonmonotonic logic: Context-dependent reasoning, pp. 61–62. Springer, Berlin (1994)
Antoniou, G., Sperschneider, V.: Operational concepts of nonmonotonic logics, part 1: Default logic. Artificial Intelligence 8(1), 3–16 (1994)
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Lin, Z., Ma, Y., Lin, Z. (2006). A Fault-Tolerant Default Logic. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds) Logics in Artificial Intelligence. JELIA 2006. Lecture Notes in Computer Science(), vol 4160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11853886_22
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DOI: https://doi.org/10.1007/11853886_22
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