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Introduction to the Philosophy and Mathematics of Algorithmic Learning Theory

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Induction, Algorithmic Learning Theory, and Philosophy

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References

  1. Angluin, D. (1980). “Inductive Inference of Formal Languages from Positive Data”, Information and Control 45, 117–135.

    Article  Google Scholar 

  2. Angluin, D. and Smith, C.H. (1983). “Inductive Inference: Theory and Methods”, Computing Surveys 15, 237–269.

    Article  Google Scholar 

  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. Blum, L. and Blum, M. (1975). “Toward a Mathematical Theory of Inductive Inference”, Information and Control 28, 125–155.

    Article  Google Scholar 

  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. Carnap, R. (1950). Logical Foundations of Probability, Chicago: University of Chicago Press.

    Google Scholar 

  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. 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. Case, J. and Smith, C. (1983). “Comparison of Identification Criteria for Machine Inductive Inference”, Theoretical Computer Science 25, 193–220.

    Article  Google Scholar 

  10. Chomsky, N. (1965). Aspects of the Theory of Syntax, Cambridge (Mass.): MIT Press.

    Google Scholar 

  11. Curd, M. and Cover, J.A. (eds.) (1998). Philosophy of Science: The Central Issues, New York: W.W. Norton.

    Google Scholar 

  12. Feyerabend, P. (1975). Against Method, London: Verso.

    Google Scholar 

  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.

    Article  Google Scholar 

  14. Giere, R. (1985) “Philosophy of Science Naturalized”, Philosophy of Science 52, 331–356.

    Article  Google Scholar 

  15. Glymour, C. (1980). Theory and Evidence, Princeton: Princeton University Press.

    Google Scholar 

  16. Gold, E.M. (1967). “Language Identification in the Limit”, Information and Control 10, 447–474.

    Article  Google Scholar 

  17. Goodman, N. (1983). Fact, Fiction, and Forecast, 4th ed., Cambridge (Mass.): Harvard University Press.

    Google Scholar 

  18. Harizanov, V.S. and Stephan, F. (2007). “On the Learnability of Vector Spaces”, Journal of Computer and System Sciences 73, 109–122.

    Article  Google Scholar 

  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. Hume, D. (1984). An Inquiry Concerning Human Understanding, Hendell, C. (ed.), New York: Bobbs-Merrill.

    Google Scholar 

  21. Jain, S. and Stephan, F. (2003). “Learning by Switching Type of Information”, Information and Computation 185, 89–104.

    Article  Google Scholar 

  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. 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. Kelly, K.T. (1996). The Logic of Reliable Inquiry, Oxford: Oxford University Press.

    Google Scholar 

  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. Kelly, K.T. (2004). “Uncomputability: The Problem of Induction Internalized”, Theoretical Computer Science 317, 227–249.

    Article  Google Scholar 

  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. Lakatos, I. (1976). Proofs and Refutations, Cambridge: Cambridge University Press.

    Google Scholar 

  29. Lakatos, I. (1998). “Science or Pseudo-Science”, in Curd, M. and Cover, J.A [11], 20–26.

    Google Scholar 

  30. Laudan, L. (1980). “Why Was the Logic of Discovery Abandoned?”, in Nickles, T. [38], 173–183.

    Google Scholar 

  31. Martin, E. and Osherson, D. (1998). Elements of Scientific Inquiry, Cambridge (Mass.): MIT Press.

    Google Scholar 

  32. Merkle, W. and Stephan, F. (2003). “Refuting Learning Revisited”, Theoretical Computer Science 298, 145–177.

    Article  Google Scholar 

  33. Minicozzi, E. (1976). “Some Natural Properties of Strong-Identification in Inductive Inference”, Theoretical Computer Science 2, 345–360.

    Article  Google Scholar 

  34. Mitchell, T.M. (1997). Machine Learning, New York: McGraw-Hill.

    Google Scholar 

  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. Mostowski, M. (2001). “On Representing Concepts in Finite Models”, Mathematical Logic Quarterly 47, 513–523.

    Article  Google Scholar 

  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. Nickles, T. (ed.) (1980). Scientific Discovery, Logic, and Rationality, Dordrectht: Reidel.

    Google Scholar 

  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. Odifreddi, P. (1989). Classical Recursion Theory, Amsterdam: North-Holland.

    Google Scholar 

  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. Osherson, D.N. and Weinstein, S. (1982). “Criteria of Language Learning”, Information and Control 52, 123–138.

    Article  Google Scholar 

  43. Popper, K. (1963). Conjectures and Refutations: The Growth of Scientific Knowledge, London: Routledge.

    Google Scholar 

  44. Putnam, H. (1963). “‘Degree of Confirmation’ and Inductive Logic”, in Putnam, H. [47], 270–292.

    Google Scholar 

  45. Putnam, H. (1965). “Trial and Error Predicates and the Solution to the Problem of Mostowski”, Journal of Symbolic Logic 30, 49–57.

    Article  Google Scholar 

  46. Putnam, H. (1975). “Probability and Confirmation”, in Putnam, H. [47], 293–304.

    Google Scholar 

  47. Putnam, H. (1975). Mathematics, Matter, and Method, Cambridge: Cambridge University Press.

    Google Scholar 

  48. Schäfer-Richter, G. (1984). Über Eingabeabhängigkeit und Komplexität von Inferenz-strategien, Aachen, Germany: PhD Dissertation, Rheinisch-Westfälische Techniche Hochschule.

    Google Scholar 

  49. Sharma, A. (1998). “A Note on Batch and Incremental Learnability”, Journal of Computer and System Sciences 56, 272–276.

    Article  Google Scholar 

  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. Stephan, F. and Ventsov, Yu. (2001). “Learning Algebraic Structures from Text”, Theoretical Computer Science 268, 221–273.

    Article  Google Scholar 

  52. Van Fraassen, B. (1981). The Scientific Image, Oxford: Clarendon Press.

    Google Scholar 

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Harizanov, V.S., Goethe, N.B., Friend, M. (2007). Introduction to the Philosophy and Mathematics of Algorithmic Learning Theory. In: Friend, M., Goethe, N.B., Harizanov, V.S. (eds) Induction, Algorithmic Learning Theory, and Philosophy. Logic, Epistemology, and the Unity of Science, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6127-1_1

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