Abstract
The main construction in this paper is an encoding of default logic into an “only knowing” logic with degrees of confidence. By imposing simple and natural constraints on the encoding we show that the “only knowing” logic can accommodate ordered default theories and that the constrained encoding implements a prescriptive interpretation of preference between defaults. An advantage of the encoding is that it provides a transparent formal rendition of such a semantics. A feature of the construction is that the generation of extensions can be carried out within the “only knowing” logic, using object level concepts alone.
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References
Baader, F., Hollunder, B.: How to Prefer More Specific Defaults in Terminological Default Logic. Technical Report RR-92-58, DFKI (December 1993)
Brewka, G.: Adding priorities and specificity to default logic. In: MacNish, C., Moniz Pereira, L., Pearce, D.J. (eds.) JELIA 1994. LNCS (LNAI), vol. 838, pp. 247–260. Springer, Heidelberg (1994)
Brewka, G., Eiter, T.: Prioritizing Default Logic. In: Hölldobler, S. (ed.) Intellectics and Computational Logic. Papers in Honor of Wolfgang Bibel. Kluwer Academic Publisher, Dordrecht (2000)
Chen, J.: The Logic of Only Knowing as a Unified Framework for Non-monotonic Reasoning. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 152–161. Springer, Heidelberg (1993)
Delgrande, J.P., Schaub, T.: Expressing Preferences in Default Logic. Artificial Intelligence 123, 41–87 (2000)
Delgrande, J.P., Schaub, T., Tompits, H., Wang, K.: A Classification and Survey of Preference Handling Approaches in Nonmonotonic Reasoning. Computational Intelligence 20(2), 308–334 (2004)
Denecker, M., Marek, V.W., Truszczynski, M.: Uniform semantic treatment of default and autoepistemic logics. Artificial Intelligence 143, 79–122 (2003)
Gottlob, G.: Complexity Results for Nonmonotonic Logics. Journal of Logic and Computation 2, 397–425 (1992)
Gottlob, G.: Translating Default Logic into Standard Autoepistemic Logic. J. ACM 42(4), 711–740 (1995)
Konolige, K.: Hierarchic Autoepistemic Theories for Nonmonotonic Reasoning. In: Proceedings of the Seventh National Conference on Artificial Intelligence (AAAI 1988), pp. 439–443. Morgan Kaufmann Publishers, San Francisco (1988)
Konolige, K.: On the relationship between default and autoepistemic logic. Artificial Intelligence 35, 343–382 (1988)
Levesque, H.J.: All I know: A study in autoepistemic logic. Artificial Intelligence 42, 263–309 (1990)
Lian, E.H., Langholm, T., Waaler, A.: Only Knowing with Confidence Levels: Reductions and Complexity. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 500–512. Springer, Heidelberg (2004)
Marek, V.W., Truszczynski, M.: Nonmonotonic logics; context dependent reasoning. Springer, Heidelberg (1993)
Moore, R.: Semantical Considerations on Nonmonotonic Logic. Artificial Intelligence 25, 75–94 (1985)
Reiter, R.: A logic for default reasoning. Artificial Intelligence 13, 81–132 (1980)
Rintanen, J.: Prioritized autoepistemic logic. In: MacNish, C., Moniz Pereira, L., Pearce, D.J. (eds.) JELIA 1994. LNCS, vol. 838, pp. 232–246. Springer, Heidelberg (1994)
Waaler, A.: Consistency proofs for systems of multi-agent only knowing. To appear in Advances in Modal Logic 5
Waaler, A., Solhaug, B.: Semantics for multi-agent only knowing (extended abstract). In: Proceedings of TARK X, pp. 109–125. ACM Digital Library (2005)
Waaler, A., Klüwer, J.W., Langholm, T., Lian, E.: Only Knowing with Degrees of Confidence. To appear in the Journal of Applied Logics with Degrees of Confidence (submitted for publication)
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Engan, I., Langholm, T., Lian, E.H., Waaler, A. (2005). Default Reasoning with Preference Within Only Knowing Logic. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2005. Lecture Notes in Computer Science(), vol 3662. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11546207_24
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DOI: https://doi.org/10.1007/11546207_24
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