Abstract
This paper analyzes differences between a numeric and symbolic approach to inductive inference. It shows the importance of existing structures in the acquisition of further knowledge, including statistical confirmation. We present a new way of looking at Hempel's paradox, in which both existing structures and statistical confirmation play a role in order to decrease the harm it does to learning. We point out some of the most important structures, and we illustrate how uncertainty does blur but does not destroy these structures. We conclude that pure symbolic as well as pure statistical learning is not realistic, but the integration of the two points of view is the key to future progress, but it is far from trivial. Our system KBG is a first-order logic conceptual clustering system; thus it builds knowledge structures out of unrelated examples. We describe the choices done in KBG in order to build these structures, using both numeric and symbolic types of knowledge. Our argument gives us firm grounds to contradict Carnap's view that induction is nothing but uncertain deduction, and to propose a refinement to Popper's “purely deductive” view of the growth of science. In our view, progressive organization of knowledge plays an essential role in the growth of new (inductive) scientific theories, that will be confirmed later, quite in the Popperian way.
Similar content being viewed by others
References
Bisson, G., “A knowledge based generalizer,” inProc. 7th ICML, Austin, pp. 9–15, 1990.
Bisson, G., KBG: a Generator of Knowledge Bases. In Kodratoff, Y. (Ed.),Machine Learning: Proc. EWSL 91, Springer-Verlag, pp. 137–137, 1991.An extended version entitled “Learning of Rule Systems by Combining Clustering and Generalization” is published in the Proceedings of the International Conference Symbolic Numeric, Data Analysis and Learning, Paris 17–20 Sept. 1991, pp. 399–415.
Buchanan, B.G. and Shortliffe, E.H.,Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project, Addison-Wesley, Reading, MA, 1984.
Carnap, R.,Logical Foundations of Probability, University of Chicago Press, 1950.
Decaestecker, C., “Incremental concept formation with attribute selection,” inProc. Fourth European Working Session on Learning, Montpellier, France, pp. 49–58. 1989.
Diday, E., Lemaire, J., Pouget, J., and Testu, F.,Eléments d'Analyse des Données, Dunod, Paris, 1985.
Diday, E.,Introduction à l'Analyse des Données Symboliques, Rapport interne INRIA, No. 1074, 1989.
Diday, E., Des Objects de l'Analyse des Données à Ceux de l'Analyse des Connaissances. In Kodratoff, Y. and Diday, E. (Eds.),Induction Symbolique et Numérique a Partir des Données, CEPADUES édition. Toulouse, pp. 9–75, 1991.
Dupré, J., Probabilistic Causality Emancipated. In French, P.A., Uehling, T.E., Jr., and Wettstein, H.K. (Eds.),Midwest Studies in Philosophy IX: Causation and Causal Theories. University of Minnesota Press, Minneapolis, pp. 169–175, 1984.
Dupré, J., “Probabilistic Causality: A Rejoinder to Ellery Eels,”Philosophy of Science vol. 57, pp. 690–698, 1990.
Duval, B. and Kodratoff, Y., A Tool for the Management of Incomplete Theories: Reasoning about Explanations. In Brazdil, P., and Konolige, K. (Eds.),Machine Learning, Meta-Reasoning and Logics. Kluwer, 1989, pp. 135–158.
Eels, E. and Sober, E., “Probabilistic Causality and the Question of Transivity,”Philosophy of Science vol. 50, pp. 35–57, 1983.
Eels, E., “Probabilistic Causal Interaction,”Philosophy of Science vol. 53, pp. 52–64, 1986.
Eels, E., “Probabilistic Causality: Reply to John Dupré,”Philosophy of Science vol. 54, pp. 105–114, 1987.
Esposito, F., Malerba, D., and Semeraro, G., “Flexible matching for noisy structural descriptions,” inProc. 12th IJCAI, Sydney, pp. 658–664, 1991.
Fisher, D.H., “Knowledge Acquisition via Incremental Conceptual Learning,”Machine Learning vol 2, pp. 139–172, 1987.
Ganascia, J.G., “AGAPE et CHARADE: deux techniques d'apprentissage symbolique appliquées à la construction de bases de connaissances,” Thèse Universitè Paris Sud, 1987.
Gennary, J., Langley, P., and Fisher, D., “Model of Incremental Concept Formation,”Artificial Intelligence Journal vol. 40, pp. 11–61, 1989.
Gluck, M.A. and Corter, J.E., “Information uncertainty, and the utility of categories,”Proc. Ann. Conf. Cognitive Sci. Soc., Irvine, CA, pp. 283–287, 1985.
Golub, G. and Van Loan, C.,Matrix Computations, John Hopkins University Press, 1983.
Hempel, C.G.,Aspects of Scientific Explanation, The Free Press, N.Y. 1965.
Holland, J.H., Holyoak, K.J., Nisbett, R.E., and Thagard, P.R.,Induction, The MIT Press, Cambridge, MA, 1986.
Kietz, J.U., “Inkrementelle und reversible Acquisition von taxonomischem Wissen,” Studienarbeit, TU Berlin, Computer Science Department, 1988.
Kodratoff, Y., Addis, T., Mantaras, R.L., Morik, K., and Plaza, E., “Four stances on knowledge acquisition and machine learning,” inProc. EWSL 91, Springer-Verlag, Porto, pp. 514–533, 1991.
Kodratoff, Y. and Ganascia, J.G., Learning as a Non-deterministic but Exact Logical Process. In Torrance, S. (Ed.),The Mind and the Machine. Ellis Horwood, pp. 182–191, 1984.
Kodratoff, Y. and Ganascia, J.G., Improving the Generalization Step in Learning. In Michalski, R.S., Carbonell, J.G., Mitchell, T.M. (Eds.),Machine Learning: An Artificial Intelligence Approach, vol. II. Morgan Kaufmann, San Mateo CA, pp. 215–244, 1986.
Kodratoff, Y., Perdrix, H., and Franova, M., “Traitement symbolique du raisonnement incertain,” Actes Congrés AFCET Materials et Logiciels pour la 5eme Generation, Paris, pp. 33–45, 1985.
Kodratoff, Y., Rouveirol, G, Tecuci, G., and Duval, B., Symbolic Approaches to Uncertainty. In Ras, Z.W. and Zemankova, M. (Eds.),INTELLIGENT SYSTEMS: State of the Art and Future Directions. Ellis Horwood, 1990.
Michalski, R.S., A Theory and Methodology of Inductive Learning. In Michalski, R.S., Carbonell, J.G., Mitchell, T.M. (Eds.),Machine Learning: An Artificial Intelligence Approach, Vol. 1. Tioga, Palo Alto, CA, pp. 83–134, 1983.
Michalski, R.S. and Kodratoff, Y., Research in Machine Learning: Recent Progress, Classification of Methods, and Future Direction. In Kodratoff, Y. and Michalski, R.S. (Eds.),Machine Learning: An Artificial Intelligence Approach, Vol. III. Morgan Kaufmann, San Mateo, pp. 3–30, 1990.
Michalski, R.S. and Stepp, R.E., Learning from Observation: Conceptual Clustering. In Michalski, R.S., Carbonell, J.G., Mitchell, T.M. (Eds.),Machine Learning: An Artificial Intelligence Approach. Morgan Kaufmann, San Mateo, pp. 331–363, 1983.
Morik, K., Acquiring Domain Models. In Boose, J. and Gaines, B. (Eds.),Knowledge Acquisition Tools for Expert Systems 2. Academic Press, 1988.
Nicolas, J., Lebbe, J., and Vignes, R., “From knowledge to similarity,” inProc. Int. Conf. Symbolic-Numeric, Data Analysis and Learning, Paris, pp. 585–597, 1991.
Peirce, C.S., “Elements of logic.” In Hartshone, C.H. and Weiss, P. (Eds.),Collected Papers of Charles Sanders Peirce (1839–1914). Harvard University Press, Cambridge MA, 1965.
Popper, K.R.,The Logic of Scientific Discovery, Harper and Row, NY, 1959.
Popper, K.R.,Objective Knowledge, Clarendon Press, Oxford, p. 364, 1972.
Quinlan, J.R., Learning Efficient Classification Procedures and Their Application to Chess End Games. In Michalski, R.S., Carbonell, J.G., Mitchell, T.M. (Eds.),Machine Learning: An Artificial Intelligence Approach. Morgan Kaufmann, San Mateo, CA, pp. 463–482, 1983.
Qunilan, J.R., “Generating production rules from decision tree,” in10th IJCAI, Milana, pp. 304–307, 1987.
Rouveirol, C., “Saturation: postponing choices when inverting resolution,” in9th European Conf. Artif. Intell. Stockholm, pp. 557–562, 1990.
Segen, J., “Graph clustering and model learning by data compression,”Proc. Seventh Int. Conf. Machine Learning, Austin, pp. 93–100, 1990.
Shafer, G.A.,Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ, 1979.
Stepp, E. and Michalski, R.S., “Conceptual Clustering of Structured Objects: A Goal-Oriented Approach,”Artificial Intelligence vol. 28, pp. 43–69, 1986.
Suppes, P., Conflicting Intuitions about Causality. InMidwest Studies in Philosophy IX, Causation and Causal Theories. University of Minnesota Press, Minneapolis, pp. 151–168, 1984.
Van Fraassen, B.C.,The Scientific Image, Clarendon Press, Oxford, 1980.
Van Fraassen, B.C., Empiricism in the Philosophy of Science. In Churchland, P.M. and Hooker, C.A. (Eds),Image of Science, The University of Chicago Press, Chicago, pp. 245–308, 1985.
Vrain, C., OGUST: A System Which Learns Using Domain Properties Expressed as Theorems. InMachine Learning: An Artificial Intelligence Approach, Vol. III, 1990.
Zadeh, L.A., “Fuzzy Sets,”Information and Control, vol. 8, pp. 338–353, 1965.
Zytkow, J.M. and Simon, H.A., “A Theory of Historical Discovery: The Construction of Componential Models,”Machine Learning vol. 1, pp. 107–136, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kodratoff, Y., Bisson, G. The epistemology of conceptual clustering: KBG, an implementation. J Intell Inf Syst 1, 57–84 (1992). https://doi.org/10.1007/BF01006414
Issue Date:
DOI: https://doi.org/10.1007/BF01006414