Abstract
This paper considers the following induction problem. Given the background knowledge B and an observation O, find a hypothesis H such that a consistent theory B ∧ H has a minimal model satisfying O. We call this type of induction brave induction. Brave induction is different from explanatory induction in ILP, which requires that O is satisfied in every model of B ∧ H. Brave induction is useful for learning disjunctive rules from observations, or learning from the background knowledge containing indefinite or incomplete information. We develop an algorithm for computing brave induction, and extend it to induction in answer set programming.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
De Raedt, L., Lavrač, N.: The many faces of inductive logic programming. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 435–449. Springer, Heidelberg (1993)
De Raedt, L., Lavrač, N.: Multiple predicate learning in two inductive logic programming setting. Journal of the IGPL 4(2), 227–254 (1996)
De Raedt, L.: Logical settings for concept-learning. Artificial Intelligence 95, 187–201 (1997)
De Raedt, L., Dehaspe, L.: Learning from satisfiability. In: Proceedings of the 9th Dutch Conference on Artificial Intelligence, pp. 303–312 (1997)
Doncescu, A., Yamamoto, Y., Inoue, K.: Biological systems analysis using inductive logic programming. In: Proceedings of the 21st International Conference on Advanced Information Networking and Applications, pp. 690–695. IEEE Computer Society, Los Alamitos (2007)
Eiter, T., Gottlob, G.: On the computational cost of disjunctive logic programming: propositional case. Annals of Mathematics and Artificial Intelligence 15, 289–323 (1995)
Eiter, T., Gottlob, G., Leone, N.: Abduction from logic programs: semantics and complexity. Theoretical Computer Science 189, 129–177 (1997)
Flach, P.A., Kakas, A.C.: Abductive and inductive reasoning: background and issues. In: Flach, P.A., Kakas, A.C. (eds.) Abduction and Induction — Essays on their Relation and Integration. Kluwer Academic, Dordrecht (2000)
Gelfond, M., Przymusinska, H., Przymusinski, T.: On the relationship between circumscription and negation as failure. Artificial Intelligence 38, 75–94 (1989)
Inoue, K.: Linear resolution for consequence finding. Artificial Intelligence 56, 301–353 (1992)
Inoue, K., Sakama, C.: A fixpoint characterization of abductive logic programs. Journal of Logic Programming 27(2), 107–136 (1996)
Inoue, K.: Automated abduction. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond. LNCS (LNAI), vol. 2408, pp. 311–341. Springer, Heidelberg (2002)
Inoue, K.: Induction as consequence finding. Machine Learning 55, 109–135 (2004)
Inoue, K., Saito, H.: Circumscription policies for induction. In: Camacho, R., King, R., Srinivasan, A. (eds.) ILP 2004. LNCS (LNAI), vol. 3194, pp. 164–179. Springer, Heidelberg (2004)
Lachiche, N.: Abduction and induction from a non-monotonic reasoning perspective. In: Flach, P.A., Kakas, A.C. (eds.) Abduction and Induction — Essays on their Relation and Integration. Kluwer Academic, Dordrecht (2000)
Lifschitz, V.: Answer set programming and plan generation. Artificial Intelligence 138, 39–54 (2002)
Minker, J.: On indefinite data bases and the closed world assumption. In: Loveland, D.W. (ed.) CADE 1982. LNCS, vol. 138, pp. 292–308. Springer, Heidelberg (1982)
McDermott, D.: Nonmonotonic logic II: nonmonotonic modal theories. Journal of the ACM 29, 33–57 (1982)
Muggleton, S.: Inverse entailment and Progol. New Generation Computing 13, 245–286 (1995)
Nienhuys-Cheng, S.-H., de Wolf, R.: Foundations of Inductive Logic Programming. LNCS (LNAI), vol. 1228. Springer, Heidelberg (1997)
Plotkin, G.D.: A note on inductive generalization. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 5, pp. 153–163. Edinburgh University Press (1970)
Reiter, R.: On closed world databases. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 55–76. Plenum, New York (1978)
Sakama, C.: Inverse entailment in nonmonotonic logic programs. In: Cussens, J., Frisch, A.M. (eds.) ILP 2000. LNCS (LNAI), vol. 1866, pp. 209–224. Springer, Heidelberg (2000)
Sakama, C.: Nonmonotonic inductive logic programming. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 62–80. Springer, Heidelberg (2001)
Sakama, C.: Induction from answer sets in nonmonotonic logic programs. ACM Transactions on Computational Logic 6(2), 203–231 (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sakama, C., Inoue, K. (2008). Brave Induction. In: Železný, F., Lavrač, N. (eds) Inductive Logic Programming. ILP 2008. Lecture Notes in Computer Science(), vol 5194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85928-4_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-85928-4_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85927-7
Online ISBN: 978-3-540-85928-4
eBook Packages: Computer ScienceComputer Science (R0)