Abstract
This paper introduces a novel logical framework for concept-learning called brave induction. Brave induction uses brave inference for induction and is useful for learning from incomplete information. Brave induction is weaker than explanatory induction which is normally used in inductive logic programming, and is stronger than learning from satisfiability, a general setting of concept-learning in clausal logic. We first investigate formal properties of brave induction, then develop an algorithm for computing hypotheses in full clausal theories. Next we extend the framework to induction in nonmonotonic logic programs. We analyze computational complexity of decision problems for induction on propositional theories. Further, we provide examples of problem solving by brave induction in systems biology, requirement engineering, and multiagent negotiation.
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Almaas, E., Kovács, B., Vicsek, T., Oltvai, Z. N., & Barabási, A. L. (2004). Global organization of metabolic fluxes in the bacterium Escherichia coli. Nature, 427, 839–843.
Alrajeh, D., Ray, O., Russo, A., & Uchitel, S. (2007). Extracting requirements from scenarios with ILP. In Lecture notes in artificial intelligence : Vol. 4455. Proceedings of the 16th international conference on inductive logic programming (pp. 64–78). Berlin: Springer.
Bossu, G., & Siegel, P. (1985). Saturation, nonmonotonic reasoning and the closed-world assumption. Artificial Intelligence, 25, 13–63.
Clark, K. L. (1978). Negation as failure. In H. Gallaire & J. Minker (Eds.), Logic and data bases (pp. 293–322). New York: Plenum.
De Raedt, L. (1997). Logical settings for concept-learning. Artificial Intelligence, 95, 187–201.
De Raedt, L., & Dehaspe, L. (1997a). Clausal discovery. Machine Learning, 26(2–3), 99–146.
De Raedt, L., & Dehaspe, L. (1997b). Learning from satisfiability. In Proceedings of the 9th Dutch conference on artificial intelligence (pp. 303–312).
De Raedt, L., & Lavrač, N. (1993). The many faces of inductive logic programming. In Lecture notes in computer science : Vol. 689. Methodologies for intelligent systems, 7th international symposium (pp. 435–449). Berlin: Springer.
De Raedt, L., & Lavrač, N. (1996). Multiple predicate learning in two inductive logic programming setting. Journal of the IGPL, 4(2), 227–254.
Eiter, T., & Gottlob, G. (1995). On the computational cost of disjunctive logic programming: propositional case. Annals of Mathematics and Artificial Intelligence, 15, 289–323.
Eiter, T., Gottlob, G., & Leone, N. (1997). Abduction from logic programs: semantics and complexity. Theoretical Computer Science, 189, 129–177.
Flach, P. A. (1996). Rationality postulates for induction. In Proceedings of the 6th international conference on theoretical aspects of rationality and knowledge (pp. 267–281). San Mateo: Morgan Kaufmann.
Flach, P. A., & Kakas, A. C. (2000). Abductive and inductive reasoning: background and issues. In P. A. Flach & A. C. Kakas (Eds.), Abduction and induction—essays on their relation and integration (pp. 1–27). Dordrecht: Kluwer Academic.
Gelfond, M., & Lifschitz, V. (1991). Classical negation in logic programs and disjunctive databases. New Generation Computing, 9, 365–385.
Gelfond, M., Przymusinska, H., & Przymusinski, T. (1989). On the relationship between circumscription and negation as failure. Artificial Intelligence, 38, 75–94.
Helft, N. (1989). Induction as nonmonotonic inference. In Proceedings of the 1st international conference on principles of knowledge representation and reasoning (pp. 149–156). San Mateo: Morgan Kaufmann.
Inoue, K. (1992). Linear resolution for consequence finding. Artificial Intelligence, 56, 301–353.
Inoue, K. (2002). Automated abduction. In Lecture notes in artificial intelligence : Vol. 2408. Computational logic: logic programming and beyond. Essays in honour of Robert A. Kowalski, part II (pp. 311–341). Berlin: Springer.
Inoue, K. (2004). Induction as consequence finding. Machine Learning, 55, 109–135.
Inoue, K., & Saito, H. (2004). Circumscription policies for induction. In Lecture notes in artificial intelligence : Vol. 3194. Proceedings of the 14th international conference on inductive logic programming (pp. 164–179). Berlin: Springer.
Inoue, K., & Sakama, C. (1996). A fixpoint characterization of abductive logic programs. Journal of Logic Programming, 27(2), 107–136.
Lachiche, N. (2000). Abduction and induction from a non-monotonic reasoning perspective. In P. A. Flach & A. C. Kakas (Eds.), Abduction and induction—essays on their relation and integration (pp. 107–116). Dordrecht: Kluwer Academic.
Lifschitz, V. (2002). Answer set programming and plan generation. Artificial Intelligence, 138, 39–54.
Marek, V. M., Niemelä, I., & Truszczyński, M. (2007). Logic programs with monotone abstract constraint atoms. Theory and Practice of Logic Programming, 8(2), 167–199.
McCarthy, J. (1980). Circumscription—a form of nonmonotonic reasoning. Artificial Intelligence, 13, 27–39.
McDermott, D. (1982). Nonmonotonic logic II: nonmonotonic modal theories. Journal of the ACM, 29, 33–57.
Minker, J. (1982). On indefinite data bases and the closed world assumption. In Lecture notes in computer science : Vol. 138. Proceedings of the 6th international conference on automated deduction (pp. 292–308). Berlin: Springer.
Muggleton, S. (1995). Inverse entailment and Progol. New Generation Computing, 13, 245–286.
Muggleton, S., & De Raedt, R. (1994). Inductive logic programming: theory and methods. Journal of Logic Programming, 19/20, 629–679.
Niemelä, I., Simons, P., & Soininen, T. (1999). Stable model semantics of weighted constraint rules. In Lecture notes in artificial intelligence : Vol. 1730. Proceedings of the 5th international conference on logic programming and nonmonotonic reasoning (pp. 317–331). Berlin: Springer.
Nienhuys-Cheng, S.-H., & De Wolf, R. (1997). Lecture notes in artificial intelligence : Vol. 1228. Foundations of inductive logic programming. Berlin: Springer.
Otero, R. P. (2001). Induction of stable models. In Lecture notes in artificial intelligence : Vol. 2157. Proceedings of the 11th international conference on inductive logic programming (pp. 193–205). Berlin: Springer.
Plotkin, G. D. (1970). A note on inductive generalization. In B. Meltzer & D. Michie (Eds.), Machine intelligence (Vol. 5, pp. 153–163). Edinburgh: Edinburgh University Press.
Ray, O. (2008). Nonmonotonic abductive inductive learning. Journal of Applied Logic. 7(3), 329–340
Reiter, R. (1978). On closed world databases. In H. Gallaire & J. Minker (Eds.), Logic and data bases (pp. 55–76). New York: Plenum.
Sakama, C. (2000). Inverse entailment in nonmonotonic logic programs. In Lecture notes in artificial intelligence : Vol. 1866. Proceedings of the 10th international conference on inductive logic programming (pp. 209–224). Berlin: Springer.
Sakama, C. (2001). Nonmonotonic inductive logic programming. In Lecture notes in artificial intelligence : Vol. 2173. Proceedings of the 6th international conference on logic programming and nonmonotonic reasoning (pp. 62–80). Berlin: Springer.
Sakama, C. (2005). Induction from answer sets in nonmonotonic logic programs. ACM Transactions on Computational Logic, 6(2), 203–231.
Sakama, C. (2008). Inductive negotiation in answer set programming. In Lecture notes in artificial intelligence : Vol. 5397. Proceedings of the 6th international workshop on declarative agent languages and technologies (pp. 143–160). Berlin: Springer.
Sakama, C., & Inoue, K. (1994). An alternative approach to the semantics of disjunctive logic programs and deductive databases. Journal of Automated Reasoning, 13(1), 145–172.
Sakama, C., & Inoue, K. (2008). Brave induction. In Lecture notes in artificial intelligence : Vol. 5194. Proceedings of the 18th international conference on inductive logic programming (pp. 261–278). Berlin: Springer.
Tamaddoni-Nezhad, A., Chaleil, R., Kakas, A. C., & Muggleton, S. (2006). Application of abductive ILP to learning metabolic network inhibition from temporal data. Machine Learning, 65, 209–230.
Yamamoto, Y., Inoue, K., & Doncescu, A. (2009, in press). Integrating abduction and induction in biological inference using CF-Induction. In H. Lodhi & S. Muggleton (Eds.), Wiley book series on bioinformatics. Elements of computational systems biology. New York: Wiley.
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Editors: Filip Zelezny and Nada Lavrac.
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Sakama, C., Inoue, K. Brave induction: a logical framework for learning from incomplete information. Mach Learn 76, 3–35 (2009). https://doi.org/10.1007/s10994-009-5113-y
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DOI: https://doi.org/10.1007/s10994-009-5113-y