Minds and Machines

, Volume 17, Issue 1, pp 47–66 | Cite as

Getting Rid of Derivational Redundancy or How to Solve Kuhn’s Problem

Article
  • 82 Downloads

Abstract

This paper deals with the problem of derivational redundancy in scientific explanation, i.e. the problem that there can be extremely many different explanatory derivations for a natural phenomenon while students and experts mostly come up with one and the same derivation for a phenomenon (modulo the order of applying laws). Given this agreement among humans, we need to have a story of how to select from the space of possible derivations of a phenomenon the derivation that humans come up with. In this paper we argue that the problem of derivational redundancy can be solved by a new notion of “shortest derivation”, by which we mean the derivation that can be constructed by the fewest (and therefore largest) partial derivations of previously derived phenomena that function as “exemplars”. We show how the exemplar-based framework known as “Data-Oriented Parsing” or “DOP” can be employed to select the shortest derivation in scientific explanation. DOP’s shortest derivation of a phenomenon maximizes what is called the “derivational similarity” between a phenomenon and a corpus of exemplars. A preliminary investigation with exemplars from classical and fluid mechanics shows that the shortest derivation closely corresponds to the derivations that humans construct. Our approach also proposes a concrete solution to Kuhn’s problem of how we know on which exemplar a phenomenon can be modeled. We argue that humans model a phenomenon on the exemplar that is derivationally most similar to the phenomenon, i.e. the exemplar from which the largest subtree(s) can be used to derive the phenomenon.

Keywords

Scientific explanation Derivational redundancy Exemplar-based reasoning Data-oriented parsing Shortest derivation Derivational similarity Kuhn’s problem 

Notes

Acknowledgments

The author is grateful to Margaret Morrison for insightful comments and suggestions on a previous version of this paper. All remaining shortcomings are entirely the author’s responsibility. This paper also benefitted from suggestions by an anonymous reviewer.

References

  1. Alonso, M., & Finn, E. (1996). Physics. Addison-Wesley.Google Scholar
  2. Baader, F., & Nipkow, T. (1998). Term rewriting and all that. Cambridge University Press.Google Scholar
  3. Bod, R. (1998). Beyond grammar: An experience-based theory of language. CSLI Publications/Cambridge University Press.Google Scholar
  4. Bod, R. (2000). Parsing with the shortest derivation. Proceedings COLING 2000, Saarbruecken, Germany, pp. 69–75.Google Scholar
  5. Bod, R. (2006). Towards a general model of applying science. International Studies in the Philosophy of Science, 20(1), 5–25.CrossRefGoogle Scholar
  6. Bod, R., Scha, R., & Sima’an, K. (eds.) (2003). Data-oriented parsing. University of Chicago Press.Google Scholar
  7. Carbonell, J. (1986). Derivational analogy: A theory of reconstructive problem solving and expertise acquisition. In R. Michalski et al. (eds.), Machine learning (Vol. II, pp. 371–392). Morgan Kaufmann.Google Scholar
  8. Cartwright, N. (1983). How the laws of physics lie. Oxford University Press.Google Scholar
  9. Cartwright, N. (1999). The dappled world. Cambridge University Press.Google Scholar
  10. Douglas, J., & Matthews, R. (1996). Fluid mechanics (Vol. 1, 3rd ed.). Longman.Google Scholar
  11. Falkenhainer, B., Forbus, K., & Gentner, D. (1989). The structure-mapping engine: Algorithm and examples. Artificial Intelligence, 41, 1–63.MATHCrossRefGoogle Scholar
  12. Friedman, M. (1974). Explanation and scientific understanding. Journal of Philosophy, 71, 5–19.CrossRefGoogle Scholar
  13. Giere, R. (1988). Explaining science: A cognitive approach. University of Chicago Press.Google Scholar
  14. Giere, R. (1999). Science without laws. The University of Chicago Press.Google Scholar
  15. Goodman, J. (2003). Efficient algorithms for the DOP model. In R. Bod, R. Scha, & K. Sima’an (eds.), Data-oriented parsing (pp. 125–146). CSLI Publications.Google Scholar
  16. Hartmann, S. (1999). Models and stories in hadron physics. In M. Morgan & M. Morrison (eds.), Models as mediators (pp. 326–346). Cambridge University Press.Google Scholar
  17. Hempel, C., & Oppenheim, P. (1948). Studies in the logic of explanation. Philosophy of Science, 15, 135–175.CrossRefGoogle Scholar
  18. Kitcher, P. (1981). Explanatory unification. Philosophy of Science, 48, 507–531.CrossRefGoogle Scholar
  19. Kitcher, P. (1989). Explanatory unification and the causal structure of the world. In P. Kitcher & W. Salmon (eds.), Scientific explanation (pp. 410–505). University of Minnesota Press.Google Scholar
  20. Kolodner, J. (1993), Case-based reasoning. Morgan Kaufmann.Google Scholar
  21. Kuhn, T. (1970). The structure of scientific revolutions, (2nd ed.), University of Chicago Press.Google Scholar
  22. Manning, C., & Schütze, H. (1999). Foundations of statistical natural language processing. The MIT Press.Google Scholar
  23. Morrison, M. (1999). Models as autonomous agents. In M. Morgan & M. Morrison (eds.), Models as mediators (pp. 38–65). Cambridge University Press.Google Scholar
  24. Nickles, T. (2003). Normal science: From logic to case-based and model-based reasoning. In T. Nickles (ed.), Thomas kuhn (pp. 142–177). Cambridge University Press.Google Scholar
  25. Norman, E., Riley, J., & Whittaker, M. (1990). Advanced design and technology. Harlow, UK:LongmanGoogle Scholar
  26. Salmon, W. (1990). Four decades of scientific explanation. University of Minneapolis Press.Google Scholar
  27. Scha, R. (1990). Language theory and language technology: Competence and performance. In Q. A. M. de Kort & G. L. J. Leerdam (eds.), Computertoepassingen in de Neerlandistiek, Almere.Google Scholar
  28. Scha, R., Bod, R., & Sima’an, K. (1999). A memory-based model of syntactic analysis: Data-oriented parsing. Journal of Experimental and Theoretical Artificial Intelligence, 11(3), 409–440.CrossRefGoogle Scholar
  29. VanLehn, K. (1998). Analogy events: How examples are used during problem solving. Cognitive Science, 22(3), 347–388.CrossRefGoogle Scholar
  30. Veloso, M., & Carbonell, J. (1993). Derivational analogy in PRODIGY: Automating case acquisition, storage, and utilization. Machine Learning, 10(3), 249–278.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of St AndrewsSt AndrewsScotland, UK
  2. 2.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations