An Interpretation of Default Logic in Minimal Temporal Epistemic Logic
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When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this interpretation yields a semantics for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours.
- Amati, G., Aiello, L.C., Gabbay, D., and Pirri, F., 1996, “A structural property on modal frames characterizing default logic,” Journal of the IGPL 4, 7–22.
- Amati, G., Aiello, L.C., and Pirri, F., 1997, “Definability and commonsense reasoning,” Artificial Intelligence 93, 169–199.
- Benthem, J.F.A.K. van, 1983, The Logic of Time: A Model Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse, Dordrecht: Reidel.
- Besnard, P., 1989, An Introduction to Default Logic, Berlin: Springer-Verlag.
- Besnard, P. and Mercer, R.E., 1992, “Non-monotonic logics: A valuations-based approach,” pp. 77–84 in Artificial Intelligence V: Methodology, Systems, Applications, B. du Boulay and V. Sgurev, eds., Amsterdam: Elsevier Science Publishers.
- Besnard, P. and Schaub, T., 1994, “Possible worlds semantics for default logics,” Fundamenta Informaticae 21, 39–66.
- Etherington, D.W., 1987, “A semantics for default logic,” pp. 495–498 in Proceedings IJCAI87, J. McDermott, ed., San Mateo, CA: Morgan Kaufmann; see also
- Etherington, D.W., 1988, Reasoning with Incomplete Information, San Mateo, CA: Morgan Kaufmann.
- Engelfriet, J., 1996, “Minimal temporal epistemic logic,” Notre Dame Journal of Formal Logic, special issue on Combining Logics 37, 233–259.
- Engelfriet, J. and Treur, J., 1993, “A temporal model theory for default logic,” pp. 91–96 in Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Proceedings ECSQARU'93, M. Clarke, R. Kruse, and S. Moral, eds., Lecture Notes in Computer Science, Vol. 747, Berlin: Springer-Verlag.
- Engelfriet, J. and Treur, J., 1994, “Temporal theories of reasoning,” pp. 279–299 in Logics in Artificial Intelligence: Proceedings of the 4th European Workshop on Logics in Artificial Intelligence, JELIA '94, C. MacNish, D. Pearce, and L.M. Pereira, eds., Berlin: Springer-Verlag. Also in Journal of Applied Nonclassical Logics 5 (1995), 239–261.
- Engelfriet, J. and Treur, J., 1996, “Semantics for default logic based on specific branching time models,” pp. 60–64 in Proceedings of the 12th European Conference on Artificial Intelligence, W. Wahlster, ed., Chichester: John Wiley & Sons.
- Engelfriet, J., Herre, H., and Treur, J., 1995, “Nonmonotonic belief state frames and reasoning frames (extended abstract),” pp. 189–196 in Symbolic and Quantitative Approaches to Reasoning and Uncertainty: Proceedings ECSQARU'95, C. Froidevaux and J. Kohlas, eds., Lecture Notes in Artificial Intelligence, Vol. 946, Berlin: Springer-Verlag.
- Finger, M. and Gabbay, D., 1992, “Adding a temporal dimension to a logic system,” Journal of Logic, Language and Information 1, 203–233.
- Gabbay, D.M., 1982, “Intuitionistic basis for non-monotonic logic,” pp. 260–273 in 6th Conference on Automated Deduction, G. Goos and J. Hartmanis, eds., Lecture Notes in Computer Science, Vol. 138, Berlin: Springer-Verlag.
- Halpern, J.Y. and Moses, Y., 1984, “Towards a theory of knowledge and ignorance,” pp. 125–143 in Proceedings of the Workshop on Non-monotonic Reasoning, AAAI'84, Menlo Park: AAAI Press.
- Hoek, W. van der, Meyer, J.—J. Ch., and Treur J., 1995, “Temporalizing epistemic default logic,” pp. 173–190 in Information Systems — Correctness and Reusability, Selected papers from the ISCORE-95 Workshop, R.B. Feenstra and R. Wieringa, eds., London: World Scientific Publishers. Extended version in Journal of Logic, Language and Information, 1998, this issue.
- Kripke, S., 1965, “Semantical analysis of intuitionistic logic I,” pp. 92–130 in Formal Systems and Recursive Function Theory, J.N. Crossley and M. Dummett, eds., Amsterdam: North-Holland.
- Levesque, H.J., 1984, “A logic of implicit and explicit belief,” pp. 198–202 in Proceedings National Conference on Artificial Intelligence, AAAI84, San Mateo, CA: Morgan Kaufmann.
- Lin, F. and Reiter, R., 1996, “Rules as actions: A situation calculus semantics for logic programs,” Journal of Logic Programming, special issue on Reasoning about Action and Change (to appear).
- Lin, F. and Shoham, Y., 1992, “A logic of knowledge and justified assumptions,” Artificial Intelligence 57, 271–289.
- Lukaszewicz, W., 1990, Non-Monotonic Reasoning: Formalization of Commonsense Reasoning, New York: Ellis Horwood.
- Marek, V.W. and Truszczynski, M., 1989, “Relating autoepistemic and default logics,” pp. 276–288 in Proceedings of the First International Conference on the Principles of Knowledge Representation and Reasoning, R.J. Brachman, H.J. Levesque, and R. Reiter, eds., San Mateo, CA: Morgan Kaufmann.
- Marek, V.W. and Truszczynski, M., 1992, “More on modal aspects of default logic,” Fundamenta Informaticae 17, 99–116.
- Marek, V.W. and Truszczynski, M., 1993, Nonmonotonic Logics; Context-Dependent Reasoning, Berlin: Springer-Verlag.
- Marek, V.W., Schwarz, G.F., and Truszczynski, M., 1993, “Modal nonmonotonic logics: Ranges, characterization, computation,” Journal of the ACM 40, 963–990.
- McDermott, D. and Doyle, J., 1980, “Nonmonotonic logic I,” Artificial Intelligence 13, 41–72.
- Reiter, R., 1980, “A logic for default reasoning,” Artificial Intelligence 13, 81–132.
- Schaub, T., 1991, “Assertional default theories: A semantical view,” pp. 496–506 in Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning, J.A. Allen, R. Fikes, and E. Sandewall, eds., San Mateo, CA: Morgan Kaufmann.
- Schwarz, G., 1995, “In search of a “true” logic of knowledge: The nonmonotonic perspective,” Artificial Intelligence 79, 39–63.
- Schwarz, G. and Truszczynski, M., 1994, “Minimal knowledge problem: A new approach,” Artificial Intelligence 67, 113–141.
- Treur, J., 1994, “Temporal semantics of meta-level architectures for dynamic control of reasoning,” pp. 353–376 in Logic Program Synthesis and Transformation — Meta-Programming in Logic: Proceedings LOPSTR'94 and META'94, L. Fribourg and F. Turini, eds., Lecture Notes in Computer Science, Vol. 883, Berlin: Springer-Verlag.
- Voorbraak, F., 1993, “Preference-based semantics for nonmonotonic logics,” pp. 584–589 in Proceedings IJCAI93, R. Bajcsy, ed., San Mateo, CA: Morgan Kaufmann.
- An Interpretation of Default Logic in Minimal Temporal Epistemic Logic
Journal of Logic, Language and Information
Volume 7, Issue 3 , pp 369-388
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- Nonmonotonic reasoning
- default logic
- temporal logic
- epistemic logic
- preferential entailment