Abstract
Inductive learning models [15] [18] often use a search space of clauses, ordered by a generalization hierarchy. To find solutions in the model, search algorithms use different generalization and specialization operators. In this article we introduce a framework for deconstructing orderings into operators. We will decompose the quasi-ordering induced by logical implication into six increasingly weak orderings. The difference between two successive orderings will be small, and can therefore be understood easily. Using this decomposition, we will describe upward and downward refinement operators for all orderings, including θ-subsumption and logical implication.
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References
M. Bain and S.H. Muggleton. Non-monotonic Learning. Machine Intelligence, 12, 1991.
W. Buntine. Generalised Subsumption and its Applications to Induction and Redundancy. Artificial Intelligence, 36(2):149–176, 1988.
N. Helft. Inductive Generalization: A Logical Framework. In I. Bratko and N. Lavrac, editor, EWSL-87, pages 149–157. Sigma Press, Wilmslow, England, 1987.
P.D. Laird. Learning from Good and Bad Data. Kluwer Academic Publishers, 1988.
S. Lapointe and S. Matwin. Subunification: A Tool for Efficient Induction of Recursive Programs. In ML-92, pages 273–280, Aberdeen, 1992. Morgan Kaufmann.
C. Lee. A completeness theorem and a computer program for finding theorems derivable from given axioms. PhD thesis, University of California, Berkely, 1967.
C. Ling and M. Dawes. SIM the Inverse of Shapiro's MIS. Technical report, Department of Computer Science, University of Western Ontario, London, Ontario, Canada., 1990.
T.M. Mitchell. Generalization as Search. Artificial Intelligence, 18:203–226, 1982.
S.H. Muggleton. Inductive logic programming. In First Conference on Algorithmic Learning Theory, Ohmsha, Tokyo, 1990. Invited paper.
S.H. Muggleton. Inverting Logical Implication. preprint, 1992.
S.H. Muggleton and C. Feng. Efficient Induction of Logic Programs. In First Conference on Algorithmic Learning Theory, Ohmsha, Tokyo, 1990.
T. Niblett. A Study of Generalisation in Logic Programs. In EWSL-88, pages 131–138. Pitman, 1988.
S.H. Nienhuys-Cheng. Generalization and Refinement. Technical report, Erasmus University Rotterdam, Dept. of Computer Science, August 1992. Preprint.
G.D. Plotkin. A Note on Inductive Generalization. Machine Intelligence, 5:153–163, 1970.
G.D. Plotkin. A Further Note on Inductive Generalization. Machine Intelligence, 6:101–124, 1971.
G.D. Plotkin. Automatic Methods of Inductive Inference. PhD thesis, Edinburgh University, Edinburgh, August 1971.
J.C. Reynolds. Transformational Systems and the Algebraic Structure of Atomic Formulas. Machine Intelligence, 5:135–153, 1970.
E.Y. Shapiro. Inductive Inference of Theories from Facts. Technical Report 192, Department of Computer Science, Yale University, New Haven. CT., 1981.
P.R.J. Van der Laag and S.H. Nienhuys-Cheng. A Locally Finite and Complete Upward Refinement Operator for θ-Subsumption. In Benelearn-93, Artificial Intelligence Laboratory, Vrije Universiteit Brussel, 1993.
P.R.J. Van der Laag and S.H. Nienhuys-Cheng. Subsumption and Refinement in Model Inference. In ECML-93, pages 95–114, 1993.
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© 1993 Springer-Verlag Berlin Heidelberg
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Nienhuys-Cheng, SH., van der Laag, P.R.J., van der Torre, L.W.N. (1993). Constructing refinement operators by decomposing logical implication. In: Torasso, P. (eds) Advances in Artificial Intelligence. AI*IA 1993. Lecture Notes in Computer Science, vol 728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57292-9_56
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DOI: https://doi.org/10.1007/3-540-57292-9_56
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