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Recursion theoretic models of learning: Some results and intuitions

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Conclusions

Very general models of learning were introduced and compared. Each of the models reflected certain situations that occur in common observations of human learning. For example, teams of learners can learn more than any individual. It was shown that sometimes to learn one concept, another must be mastered first. Sometimes, it is necessary to learn several functions simultaneously in order to learn any of them. An advantage in asking questions about the phenomenon under investigation, as opposed to waiting for data to arrive, is that it enhances learning potential. The more powerful the questions that can be formulated, the more that can be learned. Finally, it was shown that there is an advantage in some forms of procrastination in learning.

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References

  1. D. Angluin, W.I. Gasarch and C.H. Smith, Training sequences, Theor. Comp. Sci. 66(1989)255–272.

    Google Scholar 

  2. D. Angluin and C.H. Smith, Inductive inference: Theory and methods, Comp. Surveys 15(1983)237–269.

    Google Scholar 

  3. D. Angluin and C.H. Smith, Inductive inference, in:Encyclopedia of Artificial Intelligence, ed. S. Shapiro (Wiley, 1987).

  4. L. Blum and M. Blum, Toward a mathematical theory of inductive inference, Inf. Contr. 28(1975)125–155.

    Google Scholar 

  5. R.A. Brooks and A.M. Flynn, Fast, cheap and out of control: A robot invasion of the solar system, J. British Interplanet. Soc. 42(1989)478–485.

    Google Scholar 

  6. A.W. Burks,Collected Papers of Charles Sanders Peirce (Harvard University Press, Cambridge, MA, 1958).

    Google Scholar 

  7. R. Carnap,The Continuum of Inductive Methods (The University of Chicago Press, Chicago, IL, 1952).

    Google Scholar 

  8. R. Carnap and R. Jeffrey,Studies in Inductive Logic and Probability (University of California Press, Berekely, CA, 1971).

    Google Scholar 

  9. J. Case and C. Smith, Comparison of identification criteria for machine inductive inference, Theor. Comp. Sci. 25(1983)193–220.

    Google Scholar 

  10. C. Chatterjee, Cranial anatomy and relationships of a new Triassic bird from Texas, Philos. Trans. Roy. Soc. London (Biology) 332(1991)277–342.

    Google Scholar 

  11. A. Church, The constructive second number class, Bull. AMS 44(1938)224–232.

    Google Scholar 

  12. R. Freivalds and C. Smith, On the power of procrastination for machine learning, Inf. Comp. 107(1993)237–271.

    Google Scholar 

  13. M. Fulk, Prudence and other conditions on formal language learning, Inf. Comp. 85(1990)1–11.

    Google Scholar 

  14. M. Fulk and J. Case,Proc. 3rd Ann. Workshop on Computational Learning Theory (Morgan Kaufmann, Palo Alto, CA, 1990).

    Google Scholar 

  15. W. Gasarch, E. Kinber, M. Pleszkoch, C. Smith and T. Zeugmann, Learning via queries with teams and anomalies, Fundamenta Inf. 23(1995)67–89.

    Google Scholar 

  16. W. Gasarch, M. Pleszkoch and R. Solovay, Learning via queries in [+, <], J. Symb. Logic 57(1992)53–81.

    Google Scholar 

  17. W. Gasarch and C. Smith, Learning via queries, J. ACM 39(1992)649–674.

    Google Scholar 

  18. E.M. Gold, Language identification in the limit, Inf. Contr. 10(1967)447–474.

    Google Scholar 

  19. D. Haussler and L. Pitt,Proc. 1988 Workshop on Computational Learning Theory (Morgan Kaufmann, Palo Alto, CA, 1988).

    Google Scholar 

  20. J.R. Horner and J. Gorman,Digging Dinosaurs (Workman, New York, 1988).

    Google Scholar 

  21. J. Laird, P. Rosenbloom and A. Newell, Chunking in Soar: The anatomy of a general learning mechanism, Machine Learning 1(1986)11–46.

    Google Scholar 

  22. D. Osherson, M. Stob and S. Weinstein,Systems that Learn (MIT Press, Cambridge, MA, 1986).

    Google Scholar 

  23. D.N. Osherson, M. Stob and S. Weinstein, Aggregating inductive expertise, Inf. Contr. 70(1986)69–95.

    Google Scholar 

  24. L. Pitt, Probabilistic inductive inference, J. ACM 36(1989)383–433.

    Google Scholar 

  25. L. Pitt and C. Smith, Probability and plurality for aggregations of learning machines, Inf. Comp. 77(1988)77–92.

    Google Scholar 

  26. K. Popper,The Logic of Scientific Discover, 2nd Ed. (Harper Torch Books, New York, 1968).

    Google Scholar 

  27. H. Putnam, Probability and confirmation, in:Mathematics, Matter and Method, 1 (Cambridge University Press, 1975). Originally appeared in 1963 as a Voice of America Lecture.

  28. N. Rescher,Scientific Explanation (The Free Press, New York, 1970).

    Google Scholar 

  29. R. Rivest, D. Haussler and M. Warmuth,Proc. 2nd Ann. Workshop on Computational Learning Theory (Morgan Kaufmann, Palo Alto, CA, 1989).

    Google Scholar 

  30. H. Rogers, Jr.,Theory of Recursive Functions and Effective Computability (McGraw-Hill, New York, 1967).

    Google Scholar 

  31. P. Schilpp,Library of Living Philosophers: The Philosophy of Rudolph Carnap (Open Court Publ., LaSalle, IL, 1963).

    Google Scholar 

  32. C.H. Smith, The power of pluralism for automatic program synthesis, J. ACM 29(1982)1144–1165.

    Google Scholar 

  33. M. Warmuth and L. Valiant,Proc. 1991 Workshop on Computational Learning Theory (Morgan Kaufman, Palo Alto, CA, 1991).

    Google Scholar 

  34. R. Wiehagen, Limes-erkennung rekursiver funktionen durch spezielle Strategien, Elektr. Inf. verarbeit. Kybern. 12(1976)93–99.

    Google Scholar 

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Supported by NSF grants CCR 8701104 and CCR 8803641.

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Smith, C.H., Gasarch, W.I. Recursion theoretic models of learning: Some results and intuitions. Ann Math Artif Intell 15, 151–166 (1995). https://doi.org/10.1007/BF01534453

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