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Logically Reliable Inductive Inference

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Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 9))

Abstract

This paper is an overview of formal learning theory that emphasizes the philosophical motivation for the mathematical definitions. I introduce key concepts at a slow pace, comparing and contrasting with other approaches to inductive inference such as confirmation theory. A number of examples are discussed, some in detail, such as Goodman’s Riddle of Induction. I outline some important results of formal learning theory that are of philosophical interest. Finally, I discuss recent developments in this approach to inductive inference.

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References

  1. Angluin, D. (1980). “Finding Patterns Common to a Set of Strings”, Journal of Computer and System Sciences 21, 46–62.

    Article  Google Scholar 

  2. Apsitis, K. (1994). “Derived Sets and Inductive Inference”, in Arikawa, S. and Jantke, K.P. [3], 26–39.

    Google Scholar 

  3. Arikawa, S. and Jantke, K.P. (eds.) (1994). Proceedings of ALT 1994, Berlin: Springer-Verlag.

    Google Scholar 

  4. Bub, J. (1994). “Testing Models of Cognition Through the Analysis of Brain-Damaged Performance”, The British Journal for the Philosophy of Science 45, 837–855.

    Google Scholar 

  5. Carnap, R. (1952). The Continuum of Inductive Methods, Chicago: University of Chicago Press.

    Google Scholar 

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

    Article  Google Scholar 

  7. Chart, D. (2000). “Discussion: Schulte and Goodman’s Riddle”, The British Journal for the Philosophy of Science 51, 147–149.

    Article  Google Scholar 

  8. Drew, M.S. and Schulte, O. (2006). “An Algorithmic Proof That the Family Conservation Laws are Optimal for the Current Reaction Data”, High Energy Physics Preprint Archive (preprint: http://arxiv.org/abs/hep-ph/0602011).

    Google Scholar 

  9. Earman, J. (1992a). Bayes or Bust?, Cambridge (Mass.): MIT Press.

    Google Scholar 

  10. Earman, J. (ed.) (1992b). Inference, Explanation and Other Frustrations, Berkeley: University of California Press.

    Google Scholar 

  11. Freivalds, R. and Smith, C. (1993). “On the Role of Procrastination in Machine Learning”, Information and Computation 107, 237–271.

    Article  Google Scholar 

  12. Glymour, C. (1991). “The Hierarchies of Knowledge and the Mathematics of Discovery”, Minds and Machines 1, 75–95.

    Google Scholar 

  13. Glymour, C. (1994). “On the Methods of Cognitive Neuropsychology”, The British Journal for the Philosophy of Science 45, 815–835.

    Article  Google Scholar 

  14. Glymour, C. and Kelly, K. (1992). “Thoroughly Modern Meno”, in Earman, J. [10].

    Google Scholar 

  15. Gold, E.M. (1967). “Language Identification in the Limit”, Information and Control10, 447–474.

    Article  Google Scholar 

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

    Google Scholar 

  17. Hempel, C.G. (1965). Aspects of Scientific Explanation, New York: Free Press.

    Google Scholar 

  18. Houser, N. and Kloesel, C. (eds.) (1992). The Essential Peirce 1, Bloomington: Indiana University Press.

    Google Scholar 

  19. 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 

  20. James, W. (1982). “The Will to Believe”, in Thayer, H.S. [44].

    Google Scholar 

  21. Juhl, C. (1997). “Objectively Reliable Subjective Probabilities”, Synthese 109, 293–309.

    Article  Google Scholar 

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

    Google Scholar 

  23. Kelly, K. (2004). “Justification as Truth-Finding Efficiency: How Ockham’s Razor Works”, Minds and Machines 14, 485–505.

    Article  Google Scholar 

  24. Kelly K. and Schulte, O. (1995). “Church’s Thesis and Hume’s Problem”, Proceedings of the IX International Joint Congress for Logic, Methodology and the Philosophy of Science, Dordrecht: Kluwer.

    Google Scholar 

  25. Kelly, K., Schulte, O. and Juhl, C. (1997). “Learning Theory and the Philosophy of Science”, Philosophy of Science 64, 245–267.

    Article  Google Scholar 

  26. Kuhn, T.S. (1970). The Structure of Scientific Revolutions, Chicago: University of Chicago Press.

    Google Scholar 

  27. Luo, W. and Schulte, O. (2005). “Mind Change Efficient Learning”, in Learning Theory: 18th Annual Conference on Learning Theory (COLT 2005), Lecture Notes in Artificial Intelligence 3559, Auer, P. and Meir, R. (eds.), Bertinoro (Italy): Springer-Verlag, 398–412.

    Google Scholar 

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

    Google Scholar 

  29. Nozick, R. (1981). Philosophical Explanations, Cambridge (Mass.): Harvard University Press.

    Google Scholar 

  30. Osherson, D., 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 

  31. Peirce, C.S. (1878). “How to Make Our Ideas Clear”, in Houser, N. and Kloesel, C. [18], 124–141.

    Google Scholar 

  32. Putnam, H. (1963). “‘Degree of Confirmation’ and Inductive Logic”, in Schilpp, P.A. [36].

    Google Scholar 

  33. Putnam, H. (1975). “Probability and Confirmation”, in Mathematics, Matter, and Method, Cambridge: Cambridge University Press.

    Google Scholar 

  34. Reichenbach, H. (1949). The Theory of Probability, London: Cambridge University Press.

    Google Scholar 

  35. Salmon, W.C. (1991). “Hans Reichenbach’s Vindication of Induction”, Erkenntnis 35, 99–122.

    Google Scholar 

  36. Schilpp, P.A. (ed.) (1963). The Philosophy of Rudolf Carnap, La Salle (Ill.): Open Court.

    Google Scholar 

  37. Schulte, O. (1996). “Means-Ends Epistemology”, The British Journal for the Philosophy of Science 79-1, 141–147.

    Google Scholar 

  38. Schulte, O. (1999). “The Logic of Reliable and Efficient Inquiry”, The Journal of Philosophical Logic 28, 399–438.

    Article  Google Scholar 

  39. Schulte, O. (2000a). “Review of Martin and Osherson’s ‘Elements of Scientific Inquiry’”, The British Journal for the Philosophy of Science 51, 347–352.

    Article  Google Scholar 

  40. Schulte, O. (2000b). “Inferring Conservation Laws in Particle Physics: A Case Study in the Problem of Induction”, The British Journal for the Philosophy of Science 51, 771–806.

    Article  Google Scholar 

  41. Schulte, O. (2005). “Formal Learning Theory”, in Zalta, E. [46].

    Google Scholar 

  42. Schulte, O. and Drew, M.S. (2006). “Algorithmic Derivation of Additive Selection Rules and Partice Families from Reaction Data” (preprint: http://arxiv.org/abs/hep-ph/0602011).

    Google Scholar 

  43. Sklar, L. (1975). “Methodological Conservatism”, Philosophical Review LXXXIV, 374–400.

    Article  Google Scholar 

  44. Thayer, H.S. (ed.) (1982). Pragmatism, Indianapolis: Hackett.

    Google Scholar 

  45. Wei, L. and Oliver, S. (2006). Logic and Computation, 204:989–1011.

    Google Scholar 

  46. Zalta, E. (ed.) (2005). The Stanford Encyclopedia of Philosophy, Summer 2005 ed., (The Metaphysics Research Lab, Stanford University) (www-version: http://plato.stanford.edu/archives/sum2005/entries/learning-formal/).

    Google Scholar 

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Schulte, O. (2007). Logically Reliable Inductive Inference. 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_6

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