Introduction to the Philosophy and Mathematics of Algorithmic Learning Theory

  • Valentina S. Harizanov
  • Norma B. Goethe
  • Michèle Friend
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 9)


Turing Machine Belief Revision Computable Function Inductive Inference Input Stream 
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.


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  1. [1]
    Angluin, D. (1980). “Inductive Inference of Formal Languages from Positive Data”, Information and Control 45, 117–135.CrossRefGoogle Scholar
  2. [2]
    Angluin, D. and Smith, C.H. (1983). “Inductive Inference: Theory and Methods”, Computing Surveys 15, 237–269.CrossRefGoogle Scholar
  3. [3]
    Baliga, G., Case, J., Merkle, W. and Stephan, F. (2000). “Unlearning Helps”, in Montanari, U., Rolim, J.D.P. and Welzl, E. [35], 844–855.Google Scholar
  4. [4]
    Blum, L. and Blum, M. (1975). “Toward a Mathematical Theory of Inductive Inference”, Information and Control 28, 125–155.CrossRefGoogle Scholar
  5. [5]
    Carlucci, L., Case, J., Jain, S. and Stephan, F. (forth.). “U-Shaped Learning May Be Necessary”, Journal of Computer and System Sciences.Google Scholar
  6. [6]
    Carnap, R. (1950). Logical Foundations of Probability, Chicago: University of Chicago Press.Google Scholar
  7. [7]
    Case, J. and Lynes, C. (1982). “Machine Inductive Inference and Language Identification”, in Nielsen, M. and Schmidt, E.M. [39], 107–115.Google Scholar
  8. [8]
    Case, J. and Ngo Manguelle, S. (1979). “Refinements of Inductive Inference by Popperian Machines”, Technical Report 152, Buffalo: State University of New York at Buffalo.Google Scholar
  9. [9]
    Case, J. and Smith, C. (1983). “Comparison of Identification Criteria for Machine Inductive Inference”, Theoretical Computer Science 25, 193–220.CrossRefGoogle Scholar
  10. [10]
    Chomsky, N. (1965). Aspects of the Theory of Syntax, Cambridge (Mass.): MIT Press.Google Scholar
  11. [11]
    Curd, M. and Cover, J.A. (eds.) (1998). Philosophy of Science: The Central Issues, New York: W.W. Norton.Google Scholar
  12. [12]
    Feyerabend, P. (1975). Against Method, London: Verso.Google Scholar
  13. [13]
    Fulk, M., Jain, S. and Osherson, D.N. (1994). “Open Problems in ‘Systems That Learn’”, Journal of Computer and System Sciences 49, 589–604.CrossRefGoogle Scholar
  14. [14]
    Giere, R. (1985) “Philosophy of Science Naturalized”, Philosophy of Science 52, 331–356.CrossRefGoogle Scholar
  15. [15]
    Glymour, C. (1980). Theory and Evidence, Princeton: Princeton University Press.Google Scholar
  16. [16]
    Gold, E.M. (1967). “Language Identification in the Limit”, Information and Control 10, 447–474.CrossRefGoogle Scholar
  17. [17]
    Goodman, N. (1983). Fact, Fiction, and Forecast, 4th ed., Cambridge (Mass.): Harvard University Press.Google Scholar
  18. [18]
    Harizanov, V.S. and Stephan, F. (2007). “On the Learnability of Vector Spaces”, Journal of Computer and System Sciences 73, 109–122.CrossRefGoogle Scholar
  19. [19]
    Hull, D., Forbes, M. and Burian, R. (eds.) (1994). Proceedings of the 1994 Biennial Meeting of the Philosophy of Science Association, East Lansing: Philosophy of Science Association.Google Scholar
  20. [20]
    Hume, D. (1984). An Inquiry Concerning Human Understanding, Hendell, C. (ed.), New York: Bobbs-Merrill.Google Scholar
  21. [21]
    Jain, S. and Stephan, F. (2003). “Learning by Switching Type of Information”, Information and Computation 185, 89–104.CrossRefGoogle Scholar
  22. [22]
    Jain, S., Osherson, D., Royer, J.S. and Sharma, A. (1999). Systems That Learn: An Introduction to Learning Theory, 2nd ed., Cambridge (Mass.): MIT Press.Google Scholar
  23. [23]
    Jantke, K.P., Kobayashi, S., Tomita, E. and Yokomori, T. (eds.) (1993). Algorithmic Learning Theory: Proceedings of the 4th International Workshop, Lecture Notes in Computer Science 744, Berlin: Springer-Verlag.Google Scholar
  24. [24]
    Kelly, K.T. (1996). The Logic of Reliable Inquiry, Oxford: Oxford University Press.Google Scholar
  25. [25]
    Kelly, K.T. (2000). “The Logic of Success”, The British Journal for the Philosophy of Science, Special Millennium Issue 51, 639–666.Google Scholar
  26. [26]
    Kelly, K.T. (2004). “Uncomputability: The Problem of Induction Internalized”, Theoretical Computer Science 317, 227–249.CrossRefGoogle Scholar
  27. [27]
    Kelly, K. and Juhl, C. (1994). “Realism, Convergence, and Additivity”, in Hull, D., Forbes, M. and Burian, R. [19], 181–190.Google Scholar
  28. [28]
    Lakatos, I. (1976). Proofs and Refutations, Cambridge: Cambridge University Press.Google Scholar
  29. [29]
    Lakatos, I. (1998). “Science or Pseudo-Science”, in Curd, M. and Cover, J.A [11], 20–26.Google Scholar
  30. [30]
    Laudan, L. (1980). “Why Was the Logic of Discovery Abandoned?”, in Nickles, T. [38], 173–183.Google Scholar
  31. [31]
    Martin, E. and Osherson, D. (1998). Elements of Scientific Inquiry, Cambridge (Mass.): MIT Press.Google Scholar
  32. [32]
    Merkle, W. and Stephan, F. (2003). “Refuting Learning Revisited”, Theoretical Computer Science 298, 145–177.CrossRefGoogle Scholar
  33. [33]
    Minicozzi, E. (1976). “Some Natural Properties of Strong-Identification in Inductive Inference”, Theoretical Computer Science 2, 345–360.CrossRefGoogle Scholar
  34. [34]
    Mitchell, T.M. (1997). Machine Learning, New York: McGraw-Hill.Google Scholar
  35. [35]
    Montanari, U., Rolim, J.D.P. and Welzl, E. (eds.) (2000). Automata, Languages and Programming. Proceedings of the 27th International Colloquium(ICALP 2000), Lecture Notes in Computer Science 1853, Berlin: Springer-Verlag.Google Scholar
  36. [36]
    Mostowski, M. (2001). “On Representing Concepts in Finite Models”, Mathematical Logic Quarterly 47, 513–523.CrossRefGoogle Scholar
  37. [37]
    Mukouchi, Y. and Arikawa, S. (1993). “Inductive Inference Machines That Can Refute Hypothesis Spaces”, in Jantke, K.P., Kobayashi, S., Tomita, E. and Yokomori, T. [23], 123–136.Google Scholar
  38. [38]
    Nickles, T. (ed.) (1980). Scientific Discovery, Logic, and Rationality, Dordrectht: Reidel.Google Scholar
  39. [39]
    Nielsen, M. and Schmidt, E.M. (eds.) (1982). Automata, Languages and Programming: Proceedings of the 9th International Colloquium, Lecture Notes in Computer Science 140, Berlin: Springer-Verlag.Google Scholar
  40. [40]
    Odifreddi, P. (1989). Classical Recursion Theory, Amsterdam: North-Holland.Google Scholar
  41. [41]
    Osherson, D.N., Stob, M. and Weinstein, S. (1986). Systems That Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists, Cambridge (Mass.): MIT Press.Google Scholar
  42. [42]
    Osherson, D.N. and Weinstein, S. (1982). “Criteria of Language Learning”, Information and Control 52, 123–138.CrossRefGoogle Scholar
  43. [43]
    Popper, K. (1963). Conjectures and Refutations: The Growth of Scientific Knowledge, London: Routledge.Google Scholar
  44. [44]
    Putnam, H. (1963). “‘Degree of Confirmation’ and Inductive Logic”, in Putnam, H. [47], 270–292.Google Scholar
  45. [45]
    Putnam, H. (1965). “Trial and Error Predicates and the Solution to the Problem of Mostowski”, Journal of Symbolic Logic 30, 49–57.CrossRefGoogle Scholar
  46. [46]
    Putnam, H. (1975). “Probability and Confirmation”, in Putnam, H. [47], 293–304.Google Scholar
  47. [47]
    Putnam, H. (1975). Mathematics, Matter, and Method, Cambridge: Cambridge University Press.Google Scholar
  48. [48]
    Schäfer-Richter, G. (1984). Über Eingabeabhängigkeit und Komplexität von Inferenz-strategien, Aachen, Germany: PhD Dissertation, Rheinisch-Westfälische Techniche Hochschule.Google Scholar
  49. [49]
    Sharma, A. (1998). “A Note on Batch and Incremental Learnability”, Journal of Computer and System Sciences 56, 272–276.CrossRefGoogle Scholar
  50. [50]
    Soare, R.I. (1987). Recursively Enumerable Sets and Degrees. A Study of Computable Functions and Computably Generated Sets, Berlin: Springer-Verlag.Google Scholar
  51. [51]
    Stephan, F. and Ventsov, Yu. (2001). “Learning Algebraic Structures from Text”, Theoretical Computer Science 268, 221–273.CrossRefGoogle Scholar
  52. [52]
    Van Fraassen, B. (1981). The Scientific Image, Oxford: Clarendon Press.Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Valentina S. Harizanov
    • 1
  • Norma B. Goethe
    • 2
  • Michèle Friend
    • 3
  1. 1.Department of MathematicsGeorge Washington UniversityWashingtonU.S.A.
  2. 2.School of PhilosophyNational University of CordobaArgentina
  3. 3.Department of PhilosophyGeorge Washington UniversityWashingtonU.S.A.

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