Abstract
The representation formalism as well as the representation language is of great importance for the success of machine learning. The representation formalism should be expressive, efficient, useful, and applicable. First-order logic needs to be restricted in order to be efficient for inductive and deductive reasoning. In the field of knowledge representation, term subsumption formalisms have been developed which are efficient and expressive. In this article, a learning algorithm, KLUSTER, is described that represents concept definitions in this formalism. KLUSTER enhances the representation language if this is necessary for the discrimination of concepts. Hence, KLUSTER is a constructive induction program. KLUSTER builds the most specific generalization and a most general discrimination in polynomial time. It embeds these concept learning problems into the overall task of learning a hierarchy of concepts.
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References
Bisson, G. (1990). KBG, a knowledge-based generalizer. In 7th ICML-90 (pp. 9–15). Morgan Kaufmann.
Borgida, A., Brachman, R.J., McGuinness, D.L., & Resnick, L.A. (1989). Classic: a structural data model for objects. Proceedings of ACM SIGMOD-89 (pp. 58–67). Portland, OR.
Brachman, R.J., and Schmolze, J.G. (1985). An overview of the KL-ONE knowledge representation system. Cognitive Science, 9, 171–216.
Brachman, R.J. (1977). What's in a concept: structural foundations for semantic networks. International Journal of Man-Machine Studies, 9, 127–152.
Brachman, R.J., Gilbert, V.P., & Levesque, H.J. (1985). An essential hybrid reasoning system. In IJCAI-85 (pp. 532–538), Morgan Kaufmann.
Buntine, W. (1988). Generalized subsumption and its applications to induction and redundancy. Artificial Intelligence, 36, 149–176.
Ceri, S., Gottlob, G., & Tanca, L. (1990). Logic programming and databases. New York: Springer.
Cohen, W.W., Borgida, A., & Hirsh, H. (in press). Computing least common subsumers in description logic. Proceedings of AAAI-92.
Cohen, W.W., & Hirsh, H. (1992). Learnability of description logics. Proceedings of the Fourth COLT, ACM Press, pp. 116–127.
Donini, F.M., Lenzerini, M., Nardi, C., & Nutt, W. (1991). Tractble concept languages. Proceedings IJCAI-91 (pp. 458–463).
Emde, W., Habel, C. & Rollinger, C.R. (1983). The discovery of the equator or concept-driven learning. Proceedings IJCAI-83 (pp. 455–458), Morgan Kaufmann.
Fisher, D.H. (1987). Knowledge acquisition via incremental conceptual clustering, Machine Learning, 2, 139–172.
Garey, M.R., & Johnson, D.S. (1979). Computers and intractability—A guide to the theory of NP-completeness. New York: Freeman.
Haussler, D. (1989). Learning conjunctive concepts in structural domains. Machine Learning, 4, 7–40.
Kearns, M.J. (1990). The computational complexity of machine learning. Cambridge, MA, London: MIT Press.
Kietz, J.-U. (1992). A comparative study of structural most specific generalizations used in machine learning. Proceedings of ECAI'92 Workshop W18.
Kietz, J.-U. (1993). Some lower bounds for the computational complexity of inductive logic programming. Proceedings of Machine Learning ECML-93. Berlin: Springer, pp. 115–123.
Kietz, J.-U., & Wrobel, S. (1991). Controlling the complexity of learning in logic through syntactic and task-oriented models. Proceedings of Inductive Logic Programming Workshop, Porto. Also in S. Muggleton (Ed.) (1992). Inductive logic programming. New York: Academic Press, pp. 311–333.
Kietz, J.-U. (1988). Incremental and reversible acquisition of taxonomies. Proceedings of the European Knowledge Acquisition Workshop. Birlinghoven: GMD-Studien No. 143.
Kodratoff, Y., and Tecuci, G. (1989). The central role of explanations in DISCIPLE. In K. Morik (Ed.), Knowledge representation and organization in machine learning. New York: Springer, pp. 135–147.
Lebowitz, M. (1987). Experiments with incremental concept formation: UNIMEM. Machine Learning, 2, 103–138.
Luck, K.V., Nebel, B., Peltason, C., & Schmiedel, A. (1987). The anatomy of the BACK system (KIT-Report No. 41). Berlin: Technical University Berlin.
Michalski, R.S. (1983). A theory and methodology of inductive learning. In Machine learning—An artificial intelligence approach (Vol. I). Los Altos, CA: Morgan Kaufmann, pp. 83–134.
Michalski, R.S. (1990). Learning flexible concepts: fundamental ideas and a method based on two-tiered representation. In Y. Kodratoff & R.S. Michalski (Eds.), Machine Learning—An artificial intelligence approach (Vol. III). San Mateo, CA: Morgan Kaufmann, pp. 63–111.
Morik, K., & Kietz, J.-U. (1989). A bootstrapping approach to conceptual clustering. Proceedings of the Sixth International Workshop on Machine Learning, Morgan Kaufmann.
Morik, K., Wrobel, S., Kietz, J.-U., & Emde, W. (1993). Knowledge Acquisition and Machine Learning—Theory, Methods, and Applications. London: Academic Press.
Moser, M.G. (1983). An overview of NIKL, the new implementation of KL-one. In Research in knowledge representatin and natural language understanding. Cambridge, MA: B. Beranek and Newman Inc.
Muggleton, S., and Buntine, W. (1988). Machine invention of first-order predicates by inverting resolution. Proceedings of IWML-88. Ann Arbor, MI: Morgan Kaufmann.
Muggleton, S. (1990). Inductive logic programming. Proceedings of the First Conference on Algorithmic Learning Theory. Tokyo: Ohmsha.
Muggleton, S. & Feng, C. (1990). Efficient induction of logic programs. Proceedings of the First Conference on Algorithmic Learning Theory. Tokyo: Ohmsha.
Nebel, B. (1990). Reasoning and revision in hybrid representation systems. New York: Springer.
Peltason, C., Luck, K., & Kindermann, C.K. (1991). Terminological logic users workshop (KIT-Report 95). Berlin: Technical University Berlin.
Peltason, C., Schmiedel, A., Kindermann, C., & Quantz, J. (1989). The BACK System revisited (KIT-Report 75). Berlin: Technical University Berlin.
Plotkin, G.D. (1970). A note on inductive generalization. Machine Intelligence, 5, 153–163.
Quinlan, R. (1990). Learning logical defnitions from relations. Machine Learning, 5, 239–266.
Shapiro, E. (1983). Algorithmic program debugging. Cambridge, MA: MIT Press.
Stepp, R.E. & Michalski, R.S. (1986). Conceptual clustering: Inventing goal-oriented classifications of structured objects. In R. Michalski, J. Carbonell, & T. Michell (Eds.), Machine learning—An AI approach (Vol. II). San Mateo: Morgan Kaufmann, pp. 471–498.
Thompson, K., & Langley, P. (1989). Incremental concept formation with composite objects. Proceedings of the 6th International Workshop on Machine Learning, Morgan Kaufmann, pp. 373–374.
Vilain, M. (1985). The restricted language architecture of a hybrid reasoning system. IJCAI-85 (pp. 547–551).
Wrobel, S. (1987). Higher-order concepts in a tractable knowledge representation. In K. Morik (Ed.), Proceedings of the German Workshop on Artificial Intelligence. Berlin: Springer, pp. 129–138.
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Kietz, JU., Morik, K. A Polynomial Approach to the Constructive Induction of Structural Knowledge. Machine Learning 14, 193–217 (1994). https://doi.org/10.1023/A:1022626200450
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DOI: https://doi.org/10.1023/A:1022626200450