Abstract
Two levels of description of nonmonotonic reasoning are distinguished. For these levels semantical formalizations are given. The first level is defined semantically by the notion of belief state frame, the second level by the notion of reasoning frame. We introduce two specification languages to describe nonmonotonic reasoning at each of the levels: (1) a specification language for level 1, with formal semantics based on belief state frames, (2) a fragment of infinitary temporal logic as a general specification language for level 2, with formal semantics based on reasoning frames. In our framework every level 2 description can be abstracted to level 1, and for every level 1 description there are level 2 descriptions which are a specialization of it.
Part of this work has been supported by SKBS and the ESPRIT III Basic Research project 6156 DRUMS II.
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Etherington, D.W.: A Semantics for Default Logic, Proc. IJCAI-87, pp. 495–498; see also in: D.W. Etherington, Reasoning with Incomplete Information, Morgan Kaufmann, 1988
Engelfriet, J., Herre, H., Treur, J.: Nonmonotonic Belief State Frames and Reasoning Frames, in: C. Froidevaux, J. Kohlas (eds.), Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Proc. ECSQARU'95, LNAI 946, Springer-Verlag, 1995, pp. 189–196
Engelfriet, J.: Minimal Temporal Epistemic Logic, Technical Report IR-388, Vrije Universiteit Amsterdam, Department of Mathematics and Computer Science, 1995
Engelfriet, J., Treur, J.: A Temporal Model Theory for Default Logic, in: M. Clarke, R. Kruse, S. Moral (eds.), Proc. 2nd European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, ECSQARU '93, Springer Verlag, 1993, pp. 91–96. Extended version: Report IR-334, Vrije Universiteit Amsterdam, Department of Mathematics and Computer Science, 1993
Engelfriet, J., Treur, J.: Temporal Theories of Reasoning. In: C. MacNish, D. Pearce, L.M. Pereira (eds.), Logics in Artificial Intelligence, Proceedings of the 4th European Workshop on Logics in Artificial Intelligence, JELIA '94, Springer Verlag, pp. 279–299. Also in: Journal of Applied Non-Classical Logics 5 (2), 1995, pp. 239–261
Herre, H.: Compactness Properties of nonmonotonic Inference Operations. In: C. MacNish, D. Pearce, L.M. Pereira (eds.), Logics in Artificial Intelligence, Proceedings of the 4th European Workshop on Logics in Artificial Intelligence, JELIA '94, Springer Verlag, 1994, pp. 19–33. Also in: Journal of Applied Non-Classical Logics 5(1), Special Issue with selected papers from JELIA'94, 1995, pp. 121–135
Kraus, S., D. Lehmann, M. Magidor: Nonmonotonic Reasoning, Preferential models and cumulative logics; A.I. 44 (1990), 167–207
Marek, V., M. Truszczynski: Nonmonotonic Logic, Springer-Verlag, 1993
Marek, V., J. Treur, M. Truszczynski: Representation Theory for Default Logic, Proceedings of the Fourth International Symposium on Artificial Intelligence and Mathematics, 1996
Reiter, R.: A logic for default reasoning, Artificial Intelligence 13, 1980, pp. 81–132
Shoham, Y.: Nonmonotonic Logics: Meaning and Utility, In: J. McDermott (ed.), Proc. 10th International Joint Conference on Artificial Intelligence, IJCAI-87, Morgan Kaufmann, 1987, pp. 388–393
Voorbraak, F.: Preference-based Semantics for Nonmonotonic Logics, in: Bajcsy, R. (ed.), Proc. 13th International Joint Conference on Artificial Intelligence, IJCAI-93, Morgan Kaufmann, 1993, pp. 584–589
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Engelfriet, J., Treur, J. (1996). Specification of nonmonotonic reasoning. In: Gabbay, D.M., Ohlbach, H.J. (eds) Practical Reasoning. FAPR 1996. Lecture Notes in Computer Science, vol 1085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61313-7_67
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DOI: https://doi.org/10.1007/3-540-61313-7_67
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