Abstract
We formalize the notion of inverse substitution, used in the context of inverse resolution, by means of consistent term mappings. An inverse substitution from a clause to a more general clause can also be characterized by means of a term partition. We can generate clauses more general than a given clause by taking an admissible subset of its term occurrences, and constructing a term partition of this subset. We show that these term partitions can be partially ordered. This ordering coincides with the generality of the induced clauses. Similar partitions have been used by Muggleton and Buntine for describing their absorption operator. We show that their absorption algorithm is incomplete, and we give an alternative, complete algorithm, based on our definitions of admissible subset and term partition. We show that under certain conditions, clauses generated by absorption are incomparable with respect to generality. Finally, we relate this to a recent result about least general absorption obtained by Muggleton.
Chapter PDF
References
Stephen Muggleton. Inductive Logic Programming. First Conference on Algorithmic Learning Theory, Ohmsha, Tokyo, October 1990.
Stephen Muggleton & Wray Buntine. Machine Invention of First-order Predicates by Inverting Resolution. Proceedings of the 5th International Conference on Machine Learning, Morgan Kaufmann, pp. 339–351, 1988.
Shan-Hwei Nienhuys-Cheng. Consequent Functions and Inverse Resolutions. Report Eur-CS-90-03, Erasmus University, Rotterdam, Netherlands, May 1990.
Shan-Hwei Nienhuys-Cheng, Term Partitions and Minimal Generalizations of Clauses. Report, Erasmus University, Rotterdam, Netherlands, 1991.
Gordon D. Plotkin. A Note on Inductive Generalisation. Machine Intelligence 5, B. Meltzer & D. Michie (eds.), Edinburgh University Press, 1970.
John C. Reynolds. Transformational Systems and the Algebraic Structure of Atomic Formulas. Machine Intelligence 5, B. Meltzer & D. Michie (eds.), Edinburgh University Press, 1970.
Céline Rouveirol & Jean-Francois Puget. A Simple Solution for Inverting Resolution. EWSL-89, Pitman, London, pp. 201–210, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nienhuys-Cheng, S.H., Flach, P.A. (1991). Consistent term mappings, term partitions, and inverse resolution. In: Kodratoff, Y. (eds) Machine Learning — EWSL-91. EWSL 1991. Lecture Notes in Computer Science, vol 482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017030
Download citation
DOI: https://doi.org/10.1007/BFb0017030
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53816-5
Online ISBN: 978-3-540-46308-5
eBook Packages: Springer Book Archive