Abstract
Inverse entailment (IE) is a fundamental approach for hypothesis finding in explanatory induction. Some IE systems can find any hypothesis in full-clausal theories, but need several non-deterministic operators that treat the inverse relation of entailment. In contrast, inverse subsumption (IS) is an alternative approach for finding hypotheses with the inverse relation of subsumption. Recently, it has been shown that IE can be logically reduced into a new form of IS, provided that it ensures the completeness of finding hypotheses in full-clausal theories. On the other hand, it is still open to clarify how the complete IS works well in the practical point of view. For the analysis, we have implemented it with heuristic lattice search techniques used in the state-of-the-art ILP systems. This paper first sketches our IS system, and then shows its experimental result suggesting that the complete IS can practically find better hypotheses with high predictive accuracies.
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References
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)
De Raedt, L.: Logical setting for concept-learning. Artificial Intelligence 95, 187–201 (1997)
Flach, P.A.: Rationality postulates for induction. In: Proceedings of the 6th International Conference on Theoretical Aspects of Rationality and Knowledge, pp. 267–281 (1996)
Inoue, K.: Induction as consequence finding. Machine Learning 55(2), 109–135 (2004)
Inoue, K.: Linear resolution for consequence finding. Artificial Intelligence 56(2-3), 301–353 (1992)
Kimber, T., Broda, K., Russo, A.: Induction on failure: learning connected Horn theories. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 169–181. Springer, Heidelberg (2009)
Muggleton, S.H.: Inverse entailment and Progol. New Generation Computing 13, 245–286 (1995)
Muggleton, S.H., Buntine, W.L.: Machine invention of first order predicates by inverting resolution. In: Proc. of the 5th Int. Conf. on ML, pp. 339–352 (1988)
Nabeshima, H., Iwanuma, K., Inoue, K., Ray, O.: SOLAR: An automated deduction system for consequence finding. AI Commun. 23(2-3), 183–203 (2010)
Ray, O., Broda, K., Russo, A.: Hybrid abductive inductive learning: A generalisation of progol. In: Horváth, T., Yamamoto, A. (eds.) ILP 2003. LNCS (LNAI), vol. 2835, pp. 311–328. Springer, Heidelberg (2003)
Ray, O., Inoue, K.: Mode-directed inverse entailment for full clausal theories. In: Blockeel, H., Ramon, J., Shavlik, J., Tadepalli, P. (eds.) ILP 2007. LNCS (LNAI), vol. 4894, pp. 225–238. Springer, Heidelberg (2008)
Riazanov, A., Voronkov, A.: Limited Resource Strategy in Resolution Theorem Proving. Symbolic Computations 36, 101–115 (2003)
Yamamoto, A.: Hypothesis finding based on upward refinement of residue hypotheses. Theoretical Computer Science 298, 5–19 (2003)
Srinivasan, A.: The Aleph Manual. University of Oxford, Oxford (2007)
Uno, T.: A practical fast algorithm for enumerating minimal set coverings. IPSJ SIG Notes (29), 9–16 (2002)
Yamamoto, Y., Inoue, K., Doncescu, A.: Integrating abduction and induction in biological inference using CF-induction. In: Lodhi, H., Muggleton, S. (eds.) Elements of Computational Systems Biology, ch. 9, pp. 213–234 (2009)
Yamamoto, Y., Ray, O., Inoue, K.: Towards a logical reconstruction of CF-induction. In: Satoh, K., Inokuchi, A., Nagao, K., Kawamura, T. (eds.) JSAI 2007. LNCS (LNAI), vol. 4914, pp. 330–343. Springer, Heidelberg (2008)
Yamamoto, Y., Inoue, K., Iwanuma, K.: Inverse subsumption for complete explanatory induction. Machine Learning 86, 115–139 (2012)
Yamamoto, Y., Inoue, K., Iwanuma, K.: Comparison of upward and downward generalizations in CF-induction. In: Muggleton, S.H., Tamaddoni-Nezhad, A., Lisi, F.A. (eds.) ILP 2011. LNCS (LNAI), vol. 7207, pp. 373–388. Springer, Heidelberg (2012)
Tamaddoni-Nezhad, A., Muggleton, S.H.: The lattice structure and refinement operators for the hypothesis space bounded by a bottom clause. Machine Learning 76, 37–72 (2009)
Nienhuys-Cheng, S.-H., de Wolf, R. (eds.): Foundations of Inductive Logic Programming. LNCS, vol. 1228. Springer, Heidelberg (1997)
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Yamamoto, Y., Inoue, K., Iwanuma, K. (2013). Heuristic Inverse Subsumption in Full-Clausal Theories. In: Riguzzi, F., Železný, F. (eds) Inductive Logic Programming. ILP 2012. Lecture Notes in Computer Science(), vol 7842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38812-5_17
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DOI: https://doi.org/10.1007/978-3-642-38812-5_17
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