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Learning Theory and Epistemology

  • Kevin T. KellyEmail author
Part of the Springer Graduate Texts in Philosophy book series (SGTP, volume 1)

Abstract

Learning is the process of arriving at true answers to empirical questions. Learning problems, like formal problems, can be easy, hard, or unsolvable. Formal learning theory investigates the intrinsic difficulty of learning problems. This chapter summarizes some of the main concepts and results of formal learning theory, and relates them to traditional issues in epistemology.

Keywords

Input Stream Infinite Loop Probably Approximately Correct Empirical Proposition Relevant Possibility 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. Angluin, D. (1980). Inductive inference of formal languages from positive data. Information and Control, 45(2), 117–135.Google Scholar
  2. Angluin, D. (1987). Learning regular sets from queries and counterexamples. Information and Computation, 75, 87–106.CrossRefGoogle Scholar
  3. Blum, M., & Blum, L. (1975). Toward a mathematical theory of inductive inference. Information and Control, 28, 125–155.CrossRefGoogle Scholar
  4. Bonjour, L. (1985). The structure of empirical knowledge. Cambridge: Harvard University Press.Google Scholar
  5. Brown, R., & Hanlon, C. (1970). Derivational complexity and the order of acquisition of child speech. In J. Hayes (Ed.), Cognition and the development of language. New York: Wiley.Google Scholar
  6. Carnap, R. (1950). The logical foundations of probability. Chicago: University of Chicago Press.Google Scholar
  7. Case, J., & Smith, C. (1983). Comparison of identification criteria for machine inductive inference. Theoretical Computer Science, 24, 193–220.CrossRefGoogle Scholar
  8. DeFinetti. (1990). The theory of probability. New York: Wiley.Google Scholar
  9. Glymour, C. (1980). Theory and evidence. Cambridge: M.I.T. Press.Google Scholar
  10. Gold, E. M. (1965). Limiting recursion. Journal of Symbolic Logic, 30, 27–48.CrossRefGoogle Scholar
  11. Gold, E. M. (1967). Language identification in the limit. Information and Control, 10, 447–474.CrossRefGoogle Scholar
  12. Halmos, P. (1974). Measure theory. New York: Springer.Google Scholar
  13. Hinman, P. (1978). Recursion theoretic hierarchies. New York: Springer.CrossRefGoogle Scholar
  14. James, W. (1948). The will to believe. In A. Castell (Ed.), Essays in pragmatism. New York: Collier Macmillan.Google Scholar
  15. Kearns, M., & Valiant, L. (1994). Cryptographic limitations on learning boolean formulae and finite automata. Journal of the ACM, 41, 57–95.Google Scholar
  16. Kearns, M., & Vazirani, U. (1994). An introduction to computational learning theory. Cambridge: M.I.T. Press.Google Scholar
  17. Kelly, K. (1992). Learning theory and descriptive set theory. Logic and Computation, 3, 27–45.CrossRefGoogle Scholar
  18. Kelly, K. (1996). The logic of reliable inquiry. New York: Oxford University Press.Google Scholar
  19. Kelly, K., & Glymour, C. (1989). Convergence to the truth and nothing but the truth. Philosophy of Science, 56, 185–220.CrossRefGoogle Scholar
  20. Kelly, K., & Glymour, C. (1990). Theory discovery from data with mixed quantifiers. Journal of Philosophical Logic, 19, 1–33.CrossRefGoogle Scholar
  21. Kelly, K., & Glymour, C. (1992). Inductive inference from theory-laden data. Journal of Philosophical Logic, 21, 391–444.CrossRefGoogle Scholar
  22. Kelly, K., & Schulte, O. (1995). The computable testability of theories making uncomputable predictions. Erkenntnis, 43, 29–66.CrossRefGoogle Scholar
  23. Kelly, K., & Schulte, O. (1997). Church’s thesis and Hume’s problem. In M. L. Dalla Chiara et al. (Eds.), Logic and scientific methods. Dordrecht: Kluwer.Google Scholar
  24. Kemeny, J. (1953). The use of simplicity in induction. Philosophical Review, 62, 391–408.CrossRefGoogle Scholar
  25. Kugel, P. (1977). Induction pure and simple. Information and Control, 33, 236–336.Google Scholar
  26. Lauth, B. (1993). Inductive inference in the limit for first-order sentences. Studia Logica, 52, 491–517.CrossRefGoogle Scholar
  27. Lehrer, K. (1990). Theory of knowledge. San Francisco: Westview.Google Scholar
  28. Levi, I. (1991). The fixation of belief and its undoing. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  29. Miller, D. (1974). On Popper’s definitions of verisimilitude. British Journal of the Philosophy of Science, 25, 155–188.CrossRefGoogle Scholar
  30. Mormann, T. (1988). Are all false theories equally false? British Journal for the Philosophy of Science, 39, 505–519.CrossRefGoogle Scholar
  31. Neyman, J., & Pearson, E. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society, 231(A), 289–337.CrossRefGoogle Scholar
  32. Osherson, D., & Weinstein, S. (1986). Systems that learn. Cambridge: M.I.T. Press.Google Scholar
  33. Osherson, D., & Weinstein, S. (1988). Mechanical learners pay a price for Bayesianism. Journal of Symbolic Logic, 56, 661–672.CrossRefGoogle Scholar
  34. Osherson, D., & Weinstein, S. (1989a). Paradigms of truth detection. Journal of Philosophical Logic, 18, 1–41.CrossRefGoogle Scholar
  35. Osherson, D., & Weinstein, S. (1989b). Identification in the limit of first order structures. Journal of Philosophical Logic, 15, 55–81.Google Scholar
  36. Osherson, D., & Weinstein, S. (1991). A universal inductive inference machine. Journal of Symbolic Logic, 56, 661–672.CrossRefGoogle Scholar
  37. Popper, K. (1968). The logic of scientific discovery. New York: Harper.Google Scholar
  38. Popper, K. (1982). Unended quest: An intellectual autobiography. LaSalle: Open Court.Google Scholar
  39. Putnam, H. (1963). Degree of confirmation’ and inductive logic. In A. Schilpp (Ed.), The philosophy of Rudolph Carnap. LaSalle: Open Court.Google Scholar
  40. Putnam, H. (1965). Trial and error predicates and a solution to a problem of Mostowski. Journal of Symbolic Logic, 30, 49–57.CrossRefGoogle Scholar
  41. Reichenbach, H. (1938). Experience and prediction. Chicago: University of Chicago Press.Google Scholar
  42. Savage, L. (1972). The foundations of statistics. New York: Dover.Google Scholar
  43. Sextus Empiricus. (1985). Selections from the major writings on scepticism, man and god (P. Hallie, Ed., S. Etheridge, Trans.). Indianapolis: Hackett.Google Scholar
  44. Shapiro, E. (1981). Inductive inference of theories from facts. Report YLU 192. New Haven: Department of Computer Science, Yale University.Google Scholar
  45. Wexler, K., & Culicover, P. (1980). Formal principles of language acquisition. Cambridge: M.I.T. Press.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA

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