Abstract
This paper proposes a method to learn from a set of examples a theory expressed in default logic, more precisely in Lukaszewicz’default logic. The main characteristic of our method is to deal with theories where the definitions of a predicate p and definitions for its negation: ¬p are explicitly and simultaneously learned. This method relies on classical generalization techniques proposed in the field of Inductive Logic Programming and on the notion of credulous/skeptical theorem in Default Logic.
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References
F. Baader and B. Hollunder. Embedding defaults into terminological knowledge representation formalisms. In B. Nebel, C. Rich, and W. Swartout, editors, Proceedings of the Third International Conference on the Principles of Knowledge Representation and Reasoning, pages 306–317, Cambridge, MA, October 1992.
M. Bain and S. Muggleton. Non-monotonic learning. In S. Muggleton, editor, Inductive Logic Programming, pages 145–161. Academic Press, 1992.
P. Besnard. An Introduction to Default Logic. Symbolic Computation-Arti-cal Intelligence. Springer Verlag, 1989.
G. Brewka. Adding priorities and specificity to default logic. In L. Pereira and D. Pearce, editors, European Workshop on Logics in Artificial Intelligence (JELIA’94), Lecture Notes in Artificial Intelligence, pages 247–260. Springer Verlag, 1994.
P. Cholewiński, V. Marek, and M. Truszczyński. Default reasoning system DeReS. In Proceedings of the Fifth International Conference on the Principles of Knowledge Representation and Reasoning. Morgan Kaufmann Publishers, 1996.
V. Ciorba. A query answering algorithm for lukaszewicz general open defaul theory. In J.J. Alferes, L.M. Pereira, and E. Orlowska, editors, Fifth European Workshop on Logics in Artificial Intelligence (JELIA’96), volume 1126 of Lecture Notes in Artificial Intelligence. Springer Verlag, 1996.
Y. Dimopoulos, S. Dzeroski, and A. Kakas. Integrating explanatory and descriptive learning in ILP. In Proceedings of the International Joint Conference on Artificial Intelligence, volume 2, pages 900–906. Morgan Kaufmann Publishers, 1997.
Y. Dimopoulos and A. Kakas. Learning non-monotonic logic programs: Learning exceptions. In N. Lavra£ and S. Wrobel, editors, European Coonference on Machine Learning’95, volume 912 of Lecture Notes in Artificial Intelligence, pages 122–137. Springer Verlag, 1995.
D. Etherington and R. Reiter. On inheritance hierarchies with exceptions. In Proceedings of the AAAI National Conference on Artificial Intelligence, pages 104–108, 1983.
F. Bergadano, D. Gunetti, M. Nicosia, and G. Ru-o. Learning logic programs with negation as failure. In L. De Raedt, editor, Proceedings of Inductive Logic Programming conference, pages 33–51, K.U. Leuven, 1995.
M. Gelfond and V. Lifschitz. Classical negation in logic programs and disjunctive databases. New Generation Computing, 9(3-4):363–385, 1991.
K. Inoue and Y. Kudoh. Learning Extended Logic Programs. In Proceedings of the International Joint Conference on Artificial Intelligence, volume 1, pages 176–181. Morgan Kaufmann Publishers, 1997.
E. Lamma, F. Riguzzi, and L.M. Pereira. Learning with extended logic programs. In Worshop Learning Programming and non monotonic reasoning. Principles of Knowledge Representation and Reasoning, Trento, 1998.
W. Łukaszewicz. Considerations on default logic —an alternative approach. Computational Intelligence, 4:1–16, 1988.
L. Martin and C. Vrain. A three-valued framework for the induction of general logic programs. In L. De Raedt, editor, Advances in Inductive Logic Programming, pages 219–235. IOS Press, 1996.
S. Muggleton. Inductive Logic programming. Academic Press, 1992.
S. Muggleton and C. Feng. Efficient Induction of Logic Programs. In S. Muggleton, editor, Inductive Logic Programming, pages 281–298. Academic Press, 1990.
P. Nicolas and B. Duval. A theorem Prover for Lukaszewicz’Open Default Theory. In C. Froidevaux and J. Kohlas, editors, Proceedings of European Conference on Symbolic and Quantitative Approaches to Uncertainty, volume 946 of Lecture Notes in Artificial Intelligence, pages 311–319. Springer Verlag, 1995.
G.D. Plotkin. A note on Inductive Generalization. Machine Intelligence, 5:153–163, 1970.
D. Poole. Variables in hypotheses. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 905–908. Morgan Kaufmann Publishers, August 1987.
L. De Raedt and M. Bruynooghe. On negation and three-valued logic in interactice concept learning. In Proceedings of the 9th European Conference on Artificial Intelligence, pages 207–212. Pitman, 1990.
R. Reiter. A logic for default reasoning. Artificial Intelligence, 13(1-2):81–132, 1980.
R. Reiter and G. Criscuolo. On interacting defaults. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 270–276, 1981.
T. Schaub. The Automation of Reasoning with Incomplete Information: From semantic foundations to efficient computation, volume 1409 of Lecture Notes in Artificial Intelligence. Springer Verlag, 1998.
T. Schaub, S. Br:uning, and P. Nicolas. XRay: A prolog technology theorem prover for default reasoning: A system description. In J. Slaney M. McRobbie, editor, Proceedings of the Conference on Automated Deduction, volume 1104 of Lecture Notes in Artificial Intelligence, pages 293–297. Springer Verlag, 1996.
T. Schaub and M. Thielscher. Skeptical query-answering in constrained default logic. In D. Gabbay and H.-J. Ohlbach, editors, Proceedings of the International Conference on Formal and Applied Practical Reasoning, volume 1085 of Lecture Notes in Artificial Intelligence, pages 567–581. Springer Verlag, 1996.
M. Thielscher and T. Schaub. Default reasoning by deductive planning. Journal of Automated Reasonings, 15(1):1–40, 1995.
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Duval, B., Nicolas, P. (1999). Learning Default Theories. In: Hunter, A., Parsons, S. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1999. Lecture Notes in Computer Science(), vol 1638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48747-6_14
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DOI: https://doi.org/10.1007/3-540-48747-6_14
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