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A Theory and Methodology of Inductive Learning

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Machine Learning

Part of the book series: Symbolic Computation ((1064))

Abstract

The presented theory views inductive learning as a heuristic search through a space of symbolic descriptions, generated by an application of various inference rules to the initial observational statements. The inference rules include generalization rules, which perform generalizing transformations on descriptions, and conventional truth-preserving deductive rules. The application of the inference rules to descriptions is constrained by problem background knowledge, and guided by criteria evaluating the “quality” of generated inductive assertions.

Based on this theory, a general methodology for learning structural descriptions from examples, called Star, is described and illustrated by a problem from the area of conceptual data analysis.

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References

  • Amarel, S, S., “An approach to automatic theory formation,” Illinois Symposium on Principles of Self-Organization, H. von Foerster (Ed.), 1960.

    Google Scholar 

  • Banerji, R. B., “The description list of concepts,” J.A.C.M, 1962.

    Google Scholar 

  • Banerji, R. B., Artificial Intelligence: A Theoretical Perspective, Elsevier North Holland, New York, 1980.

    Google Scholar 

  • Biermann, A. W., “The inference of regular LISP programs from examples,” IEEE Transcations on Systems, Man, and Cybernetics, Vol. SMC-8, No. 8, pp. 585–600, August 1978.

    Article  MathSciNet  MATH  Google Scholar 

  • Biermann, A. and Feldman, J., A survey of results in grammatical inference, Academic Press, New York, 1972.

    Google Scholar 

  • Bongard, N., Pattern Recognition, Spartan Books, New York, 1970, (Translation from Russian original, published in 1967 ).

    Google Scholar 

  • Brachman, R. J., “On the epistemological status of semantic networks,” Associative Networks, N. V. Findler (Ed.), New York: Academic Press, 1979.

    Google Scholar 

  • Bruner, J. S., Goodnow, J. J. and Austin, G. A., A Study of Thinking, Wiley, New York, 1956.

    Google Scholar 

  • Buchanan, B. G. and Feigenbaum, E. A., “DENDRAL and Meta-DENDRAL: their applications dimension,” Artificial Intelligence, Vol. 11, pp. 5–24, 1978.

    Article  Google Scholar 

  • Buchanan, B. G., Mitchell, T. M., Smith, R. G. and Johnson, C. R. Jr., “Models of Learning Systems”, Technical Report STAN-CS-79–692, Stanford University, Computer Science Dept., January 1979.

    Google Scholar 

  • Burstall, R. M. and Darlington, J., “A transformation system for developing recursive programs,” Journal of the ACM, Vol. 24, No. 1, pp. 44–67, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  • Carnap, R, R., “The aim of inductive logic,” Logic, Methodology and Philosophy of Science, Nagel, E., Suppes, P. and Tarski, A. (Eds.), Stanford University Press, Stanford, pp. 303–318, 1962.

    Google Scholar 

  • Case, J. and Smith, C., “Comparison of identification criteria for mechanized inductive inference”, Technical Report TR-154, Dept. Computer Science., State U. of New York at Buffalo, 1981.

    Google Scholar 

  • Chang, C., and Lee, R. C., Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.

    MATH  Google Scholar 

  • Cohen, B. L., “A powerful and efficient structural pattern recognition system,” Artificial Intelligence, Vol. 9, No. 3, December 1977.

    Google Scholar 

  • Coulon, D. and Kayser, D., “Learning criterion and inductive behavior,” Pattern Recognition, Vol. 10, No. 1, pp. 19–25, 1978.

    Article  Google Scholar 

  • Davis, R. and Lenat, D. B., Knowledge Based Systems in Artificial Intelligence, McGraw Hill, New York, 1981.

    Google Scholar 

  • Dietterich, T., “Description of inductive program INDUCE 1.1”, Technical Report (Internal), Depart- ment of Computer Science, University of Illinois, Urbana-Champaign, October 1978.

    Google Scholar 

  • Dietterich, T. G., “The methodology of knowledge layers for inducing descriptions of sequentially ordered events,” Master’s thesis, University of Illinois, Urbana, October 1979.

    Google Scholar 

  • Feigenbaum E. A., “The simulation of verbal learning behavior,” Computers and Thought, Feigenbaum, E. A. and Feldman, J. (Eds.), McGraw-Hill Book Company, New York, NY, 1963.

    Google Scholar 

  • Fikes, R. E., Hart, P. E. and Nilsson, N. J., “Learning and executing generalized robot plans,” Artificial Intelligence, Vol. 3, pp. 251–288, 1972.

    Article  Google Scholar 

  • Gaines, B. R., “Maryanski’s grammatical inferencer,” IEEE Trans on Computers, Vol. C-28, pp. 62–64, 1979.

    Google Scholar 

  • Gaschnig, J., “Development of Uranium Exploration Models for Prospector Consultant System”, Internal, SRI International, March 1980.

    Google Scholar 

  • Hâjek, P. and Havrânek, T., Mechanizing Hypothesis Formation: Mathematical Foundations for a General Theory, Springer-Verlag, 1978.

    Google Scholar 

  • Hâjek, P., Havel, I., and Chytil, M., “The GUHA method of automatic hypothesis determination,” Computing, No. 1, pp. 293–308, March 1966.

    Article  MATH  Google Scholar 

  • Hayes-Roth, F., “A structural approach to pattern learning and the acquisition of classificatory power,” Proceedings of the First International Joint Conference on Pattern Recognition, Washington, D. C., pp. 343–355, 1973.

    Google Scholar 

  • Hayes-Roth, F. and McDermott, J., “An interference matching technique for inducing abstractions,” Communications of the ACM, Vol. 21, No. 6, pp. 401–410, 1978.

    Article  MATH  Google Scholar 

  • Hedrick, C. L., A Computer Program to Learn Production Systems Using a Semantic Net, Ph.D. dissertation, Carnegie-Mellon University, July 1974, ( Department of Computer Science).

    Google Scholar 

  • Hintzman, D. L., The Psychology of Learning and Memory, W. H. Freeman and Company, 1978.

    Google Scholar 

  • Hoff, B., Michalski, R. S., and Stepp, R., “INDUCE 2 - a program for learning structural descrip- tions from examples”, Technical Report 82–5, Intelligent Systems Group, October 1982.

    Google Scholar 

  • Hovland, C. I., “A ‘Communication Analysis’ of Concept Learning,” Psychological Review, pp. 461–472, November 1952.

    Google Scholar 

  • Hunt, E. B., Marin, J. and Stone, P. T., Experiments in Induction,Academic Press, New York, I966.

    Google Scholar 

  • Jouannaud, J. P., and Kodratoff, Y., “An automatic construction of LISP programs by transformations of functions synthesized from their input-output behavior,” International Journal of Policy Analysis and Information Systems, Vol. 4, No. 4, pp. 331–358, December 1980.

    MathSciNet  Google Scholar 

  • Kemeni, T. G., “The use of simplicity in induction,” Psychological Review, Vol. 62, No. 3, pp. 391–408, 1953.

    Google Scholar 

  • Kochen, M., “Experimental study of hypothesis formation by computer,” Proc. 1960 London Symp. on Information Theory, 1960.

    Google Scholar 

  • Langley, P. W., Neches, R., Neves, D. and Anzai, Y., “A domain-independent framework for procedure. learning,” Journal of Policy Analysis and Information Systems, Vol. 4, No. 2, pp. 163–197, June 1980.

    Google Scholar 

  • Larson, J., Inductive inference in the variable-valued predicate logic system VL2I: methodology and computer implementation, Ph.D. dissertation, University of Illinois, Urbana, Illinois, May 1977.

    Google Scholar 

  • Larson, J. and Michalski, R. S., “Inductive inference of VL decision rules,” Proceedings of the Workshop on Pattern Directed Inference Systems, SIGART Newsletter 63, pp. 38–44, June 1977.

    Article  Google Scholar 

  • Lenat, D. B., AM: an artificial intelligence approach to discovery in mathematics as heuristic search, Ph.D. dissertation, Stanford University, Stanford, California, 1976.

    Google Scholar 

  • Michalski, R. S. S., “A Variable-Valued Logic System as Applied to Picture Description and Recognition,” Graphic Languages, F. Nake and A. Rosenfeld (Ed.), North-Holland Publishing Co., pp. 20–47, 1972.

    Google Scholar 

  • Michalski, R. S., “AQVAL/1 - Computer implementation of a variable valued logic system VLI and examples of its application to pattern recognition,” Proceedings of the First International Joint Conference on Pattern Recognition, Washington, D. C., pp. 3–17, 19736.

    Google Scholar 

  • Michalski, R. S. S., “Variable-Valued Logic and its Applications to Pattern Recognition and Machine Learning,” Multiple-Valued Logic and Computer Science, Rine, D. (Ed.), North-Holland, pp. 506–534, 1975a.

    Google Scholar 

  • Michalski, R. S., “Synthesis of optimal and quasi-optimal variable-valued logic formulas,” Proceedings of the 1975 International Symposium on Multiple-Valued Logic,Bloomington, Indiana, pp. 76–87, May 19756.

    Google Scholar 

  • Michalski, R. S., “Pattern recognition as rule-guided inductive inference,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-2, No. 4, pp. 349–361, 1980a.

    Article  MathSciNet  Google Scholar 

  • Michalski, R. S., “Knowledge Acquisition Through Conceptual Clustering: A Theoretical Framework and an Algorithm for Partitioning Data into Conjunctive Concepts,” Policy Analysis and Information Systems,Vol. 4, No. 3, pp. 219–244, 1980c, (A Special Issue on Knowledge Acquisition and Induction).

    Google Scholar 

  • Michalski, R. S. and Chilausky, R. L., “Learning by being told and learning from examples: an experimental comparison of the two methods of knowledge acquisition in the context of developing an expert system for soybean disease diagnosis,” Policy Analysis and Information Systems, Vol. 4, No. 2, pp. 125–160, June 1980, ( Special issue on knowledge acquisition and induction).

    Google Scholar 

  • Michalski, R. S. and Larson, J. B. B., “Selection of most representative training examples and incremental generation of VLF hypotheses: the underlying methodology and the description of programs ESEL and AQ11”, Technical Report 867, Computer Science Department, University of Illinois, 1978.

    Google Scholar 

  • Michalski, R. S., and Negri, P, P., “An Experiment on Inductive Learning in Chess End Games,” Machine Representation of Knowledge, Machine Intelligence 8, E. W. Elcock and D. Michie (Ed.), Ellis Horwood, pp. 175–192, 1977.

    Google Scholar 

  • Michalski, R. S., Stepp, R., and Diday, E, E., “A recent advance in data analysis: clustering objects into clisses characterized by conjunctive concepts,” Progress in Pattern Recognition, L. Kanal and A. Rosenfeld (Ed.), North-Holland, Amsterdam, pp. 33–56, 1981.

    Google Scholar 

  • Michie, D, D., “New face of AI”, Technical Report 33, University of Edinburgh, 1977.

    Google Scholar 

  • Minsky, M, M., “A framework for representing knowledge,” The Psychology of Computer Vision, P. H. Winston (Ed.), McGraw-Hill, New York, ch. 6, pp. 211–277, 1975.

    Google Scholar 

  • Mitchell, T. M., Version Spaces: An Approach to Concept Learning, Ph.D. dissertation, Stanford University, December 1978.

    Google Scholar 

  • Moraga, C, C., “A didactic experiment in pattern recognition”, Technical Report AIUD-PR-8101, Dartmund University, 1981.

    Google Scholar 

  • Morgan, C. G., “Automated hypothesis generation using extended inductive resolution,” Advance Papers of Fourth International Joint Conference on Artificial Intelligence, Tbilisi, USSR, pp. 351–356, September 1975.

    Google Scholar 

  • Newell, A., Shaw, J. C. and Simon, H. A., “A variety of intelligent learning in a general problem solver,” Self Organizing Systems, Yovits and Cameron (Eds.), Pergamon Press, New York, 1960.

    Google Scholar 

  • Nilsson, N. J., Priciples of Artificial Intelligence, Tioga Publishing Co., 1980.

    Google Scholar 

  • O’Rorke, P., “A comparative study of inductive learning systems AQ11 and ID3”, Intelligent Systems Group Report 82–2, Department of Computer Science, University of Illinois at Urbana-Champaign, 1982.

    Google Scholar 

  • Pettorossi, A., “An Algorithm for Reducing Memory Requirements in Recursive Programs Using Annotations,” International Workshop on Program Construction, September 1980.

    Google Scholar 

  • Plotkin, G. D. D., “A further note on inductive generalization,” Machine Intelligence, Meltzer, B. and Michie, D. (Eds.), Elsevier, Edinburgh, pp. 101–124, 1971.

    Google Scholar 

  • Pokorny, D., “Knowledge Acquisition by the GUHA Method,” International Journal of Policy Analysis and Information Systems,Vol. 4, No. 4, pp. 379–399, 1980, (A special issue on knowledge acquisition and induction).

    Google Scholar 

  • Polya, G., Mathematics and Plausible Reasoning, Princeton University Press, Princeton, N.J., 1954.

    Google Scholar 

  • Popper, K., The Logic of Scientific Discovery,Harper and Row, New York, 1968, (2nd edition).

    Google Scholar 

  • Post, H. R., “Simplicity of Scientific Theories,” British Journal for the Philosophy of Science, Vol. 11, No. 41, 1960.

    Google Scholar 

  • Quinlan, J. R., “Discovering rules from large collections of examples: a case study,” Expert Systems in the Micro Electronic Age, Michie, D. (Ed.), Edinburgh University Press, Edinburgh, 1979.

    Google Scholar 

  • Russell, B., History of Western Philosophy, George Allen and Unwin, London, 1946.

    Google Scholar 

  • Sammut, C., Learning Concepts by Performing Experiments, Ph.D. dissertation, University of New South Wales, November 1981.

    Google Scholar 

  • Shapiro, Ehud Y., “Inductive Inference of Theories From Facts”, Research Report 192, Yale University, February 1981.

    Google Scholar 

  • Shapiro, A. and Niblett, T, T., “Automatic Induction of classification rules for a chess endgame,” Advances in Computer Chess, volume 3, Clarke, M.R.B. (Ed.), Edinburgh University Press, 1982.

    Google Scholar 

  • Shaw, D. E., Swartout, W. R. and Green, C. C., “Inferring LISP programs from examples,” Fourth International Joint Conference on Artificial Intelligence, Tbilisi, USSR, pp. 351–356, September 1975.

    Google Scholar 

  • Shortliffe, E., Computer Based Medical Consultations: MYCIN, New York: Elsevier, 1976.

    Google Scholar 

  • Simon, H. A. and Kotovsky, K., “Human acquisition of concepts for sequential patterns,” Psychological Review, Vol. 70, pp. 534–546, 1963.

    Article  Google Scholar 

  • Simon, H. A. and Lea, G., “Problem solving and rule induction: A unified view,” Knowledge and Cognition, L. Gregg (Ed.), Lawrence Erlbaum Associates, Hillsdale, N.J., 1974.

    Google Scholar 

  • Smith, D. R., “A Survey of the Synthesis of LISP Programs from Examples”, Technical Report, Duke University, Bonas, France, September 1980.

    Google Scholar 

  • Solomonoff, R. J., “A Formal Theory of Inductive Inference,” Information and Control, Vol. 7, 1964.

    Google Scholar 

  • Soloway, E. M. and Riseman, E. M., “Levels of pattern description in learning,” Fifth International Joint Conference on Artificial Intelligence, Cambridge, Mass., pp. 801–811, 1977.

    Google Scholar 

  • Stepp, R., “The investigation of the UNICLASS inductive program AQ7UNI and User’s Guide”, Technical Report 949, Department of Computer Science, University of Illinois, Urbana, Illinois, November 1978.

    Google Scholar 

  • Stoffel, J. C., “The theory of prime events: data analysis for sample vectors with inherently discrete variables,” Information Processing 74, North-Holland, Amsterdam, pp. 702–706, 1974.

    Google Scholar 

  • Suppes, P., Introduction to Logic, Van Nostrand Co., Princeton, 1957.

    MATH  Google Scholar 

  • Vere, S. A. A., “Induction of concepts in the predicate calculus,” Proceedings of the Fourth International Joint Conference on Artificial Intelligence, UCAI, Tbilisi, USSR, 1975.

    Google Scholar 

  • Waterman, D. A., “Generalized learning techniques for automating the learning of heuristics,” Artificial Intelligence, Vol. 1, No. 1–2, pp. 121–170, Spring 1970.

    MATH  Google Scholar 

  • Winston, P., Learning Structural Descriptions from Examples, Ph.D. dissertation, MIT, September 1970.

    Google Scholar 

  • Winston, P. H., Artificial Intelligence, Addison-Wesley, 1977.

    Google Scholar 

  • Yau, K. C., and Fu, K. S., “Syntactic shape recognition using attributed grammars,” Proceedings of the Eighth Annual EIA Symposium on Automatic Imagery Pattern Recognition, 1978.

    Google Scholar 

  • Zagoruiko, N. G., Mietody obnaruzhenia zakonomiernostiej (Methods for revealing regularities in data), Izd. Nauka, Moscow, 1981.

    Google Scholar 

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Michalski, R.S. (1983). A Theory and Methodology of Inductive Learning. In: Michalski, R.S., Carbonell, J.G., Mitchell, T.M. (eds) Machine Learning. Symbolic Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12405-5_4

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  • DOI: https://doi.org/10.1007/978-3-662-12405-5_4

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