Abstract
CF-induction is a sound and complete hypothesis finding procedure for full clausal logic which uses the principle of inverse entailment to compute a hypothesis that logically explains a set of examples with respect to a prior background theory. Currently, CF-induction computes hypotheses by applying combinations of several complex generalisation operators to an intermediate theory called a bridge formula. In this paper we propose an alternative approach whereby hypotheses are derived from a bridge formula using a single deductive operator and a single inductive operator. We show that our simplified procedure preserves the soundness and completeness of CF-induction.
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
Badea, L.: A Refinement Operator for Theories. In: Rouveirol, C., Sebag, M. (eds.) ILP 2001. LNCS (LNAI), vol. 2157, pp. 1–14. Springer, Heidelberg (2001)
Cox, P.T., Pietrzykowski, T.: A Complete, Nonredundant Algorithm for Reversed Skolemization. Theoretical Computer Science 28(3), 239–261 (1984)
Doncescu, A., Inoue, K., Yamamoto, Y.: Knowledge Based Discovery in Systems Biology Using CF-Induction. In: Okuno, H.G., Ali, M. (eds.) IEA/AIE 2007. LNCS (LNAI), vol. 4570, pp. 395–404. Springer, Heidelberg (2007)
Inoue, K.: Linear Resolution for Consequence Finding. Artificial Intelligence 56(2-3), 301–353 (1992)
Inoue, K.: Induction as Consequence Finding. Machine Learning 55(2), 109–135 (2004)
Laird, P.D.: Learning from Good and Bad Data. Kluwer Academic Publishers, Dordrecht (1988)
Lee, C.T.: A Completeness Theorem and Computer Program for Finding Theorems Derivable from Given Axioms. PhD thesis, Dept. of Electronic Eng. and Computer Sci., Univ. of California, Berkeley, CA (1967)
Midelfart, H.: A Bounded Search Space of Clausal Theories. In: Džeroski, S., Flach, P.A. (eds.) ILP 1999. LNCS (LNAI), vol. 1634, pp. 210–221. Springer, Heidelberg (1999)
Muggleton, S.H.: Inverse Entailment and Progol. New Generation Computing 13(3-4), 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 Machine Learning, pp. 339–352 (1988)
Muggleton, S.H., De Raedt, L.: Inductive Logic Programming: Theory and Methods. Logic Programming 19(20), 629–679 (1994)
Nienhuys-Cheng, S., de Wolf, R.: Foundations of Inductive Logic Programming. LNCS, vol. 1228. Springer, Heidelberg (1997)
Plotkin, G.D.: A Further Note on Inductive Generalization. In: Machine Intelligence, vol. 6, pp. 101–124. Edinburgh University Press (1971)
Ray, O., Broda, K., Russo, A.M.: 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: Proc. of the 17th Int. Conf. on Inductive Logic Programming ILP 2007. LNCS, vol. 4894. Springer, Heidelberg (to appear 2008)
Satoh, K., Uno, T.: Enumerating Maximal Frequent Sets Using Irredundant Dualization. In: Grieser, G., Tanaka, Y., Yamamoto, A. (eds.) DS 2003. LNCS (LNAI), vol. 2843, pp. 256–268. Springer, Heidelberg (2003)
Yamamoto, A.: Hypothesis Finding Based on Upward Refinement of Residue Hypotheses. Theoretical Computer Science 298, 5–19 (2003)
Yamamoto, A., Fronhöfer, B.: Hypotheses Finding via Residue Hypotheses with the Resolution Principle. In: Arimura, H., Sharma, A.K., Jain, S. (eds.) ALT 2000. LNCS (LNAI), vol. 1968, pp. 156–165. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yamamoto, Y., Ray, O., Inoue, K. (2008). Towards a Logical Reconstruction of CF-Induction. In: Satoh, K., Inokuchi, A., Nagao, K., Kawamura, T. (eds) New Frontiers in Artificial Intelligence. JSAI 2007. Lecture Notes in Computer Science(), vol 4914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78197-4_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-78197-4_31
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78196-7
Online ISBN: 978-3-540-78197-4
eBook Packages: Computer ScienceComputer Science (R0)