Advertisement

Determination, Uniformity, and Relevance: Normative Criteria for Generalization and Reasoning by Analogy

  • Todd R. Davies
Chapter
Part of the Synthese Library book series (SYLI, volume 197)

Abstract

If an agent is to apply knowledge from its past experience to a presen episode, it must know what properties of the past situation can justifiably be projected onto the present on the basis of the known similarity between the situations. The problem of specifying when to generalize or reason by analogy, and when not to, therefore looms large for the designer of a learning system. One would like to be able to program into the system a set of criteria for rule formation from which the system can correctly generalize from data as they are received. Otherwise, all of the necessary rules the agent or system uses must be programmed in ahead of time, so that they are either explicitly represented in the knowledge base or derivable from it.

Keywords

Free Variable Analogical Reasoning Polar Variable Determination Relation Determination Rule 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baker, M. and Burstein, M. H. (1987), ‘Implementing a model of human plausible reasoning’, in Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87), Los Altos, CA: Morgan Kaufmann, pp. 185–188.Google Scholar
  2. Barwise, J. and Perry, J. (1983), Situations and Attitudes, Cambridge, MA: MIT Press.Google Scholar
  3. Burstein, M. H. (1983), ‘A model of incremental analogical reasoning and debugging’, in Proceedings of the National Conference on Artificial Intelligence (AAAI-83), Los Altos, CA: Morgan Kaufmann, pp. 45–48.Google Scholar
  4. Carbonell, J. G. (1983), ‘Derivational analogy and its role in problem solving’, in Proceedings of the National Conference on Artificial Intelligence (AAAI-83), Los Altos, CA: Morgan Kaufmann, pp. 64–69.Google Scholar
  5. Carbonell, J. G. (1986), ‘Derivational analogy: A theory of reconstructive problem solving and expertise acquisition’, in Michalski, R. S., Carbonell, J. G. and Mitchell, T. M. (eds.), Machine Learning: An Artificial Intelligence Approach, Volume II. Los Altos, CA: Morgan Kaufmann, pp. 371–392.Google Scholar
  6. Carnap, R. (1963), Logical Foundations of Probability, Chicago: University of Chicago press.Google Scholar
  7. Copi, I. M. (1972), Introduction to Logic, New York: The Macmillan Company.Google Scholar
  8. Davies, T. (1985), Analogy, Informal Note No. IN-CSLI-85–4, Center for the Study of Language and Information, Stanford, CA.Google Scholar
  9. Davies, T. R. and Russell, S. J. (1987), ‘A logical approach to reasoning by analogy’, in Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87), Los Altos, CA: Morgan Kaufmann, pp. 264–270.Also issued as Technical Note 385, Artificial Intelligence Center, SRI International, Menlo Park, CA, July 1987.Google Scholar
  10. Genesereth, M. R. and Nilsson, N. J. (1987), Logical Foundations of Artificial Intelligence, Los Altos, CA: Morgan Kaufmann.Google Scholar
  11. Gentner, D. (1983), ‘Structure mapping: A theoretical framework for analogy’, Cognitive Science 7: 155–170.CrossRefGoogle Scholar
  12. Georgeff, M. P. (1987), Many Agents Are Better Than One, Technical Note 417, Artificial Intelligence Center, SRI International, Menlo Park, CA.Google Scholar
  13. Gick, M. L. and Holyoak, K. J. (1983), Schema induction and analogical transfer’, Cognitive Psychology 15: 1–38.CrossRefGoogle Scholar
  14. Goodman, L. A. and Kruskal, W. H. (1979), Measures of Association for Cross Classifications, New York: Springer-Verlag.CrossRefGoogle Scholar
  15. Goodman, N. (1983), Fact, Fiction, and Forecast, Cambridge, MA: Harvard University Press.Google Scholar
  16. Greiner, R. (1985), Learning by Understanding Analogies, Technical Report STAN-CS8 5–1071, Stanford University, Stanford, CA.Google Scholar
  17. Haberman, S. J. (1982), ‘Association, measures of’, in Kotz, S. and Johnson, N. L. (eds.), Encyclopedia of Statistical Science, Volume I, New York: John Wiley and Sons, pp. 130–137.Google Scholar
  18. Hays, W. L. and Winkler, R. L. (1970), Statistics, Volume II: Probability, Inference, and Decision, San Francisco: Holt, Rinehart and Winston.Google Scholar
  19. Hesse, M. B. (1966), Models and Analogies in Science, Notre Dame: University of Notre Dame Press.Google Scholar
  20. Holland, J., Holyoak, K., Nisbett, R. and Thagard, P. (1986), Induction: Processes of Inference, Learning, and Discovery, Cambridge, MA: MIT Press.Google Scholar
  21. Johnson, R. A. and Wichern, D. A. (1982), Applied Multivariate Statistical Analysis, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  22. Kedar-Cabelli, S. (1985), `Purpose-directed analogy’, in The Seventh Annual Conference of the Cognitive Science Society, Hillsdale, NJ: Lawrence Erlbaum Associates, pp. 150–159.Google Scholar
  23. Leblanc, H. (1969), ‘A rationale for analogical inference’, Philosophical Studies 20: 29–31.CrossRefGoogle Scholar
  24. Marr, D. (1982), Vision, New York: W. H. Freeman and Company.Google Scholar
  25. Mill, J. S. (1900), A System of Logic, New York: Harper & Brothers Publishers.Google Scholar
  26. Mitchell, T. M. (1980), The Need for Biases in Learning Generalizations, Technical Report CBM-TR-117, Rutgers University, New Brunswick, NJ.Google Scholar
  27. Mitchell, T. M., Keller, R. M., and Kedar-Cabelli, S. T. (1986), ‘Explanation-based generalization: A unifying view’, Machine Learning 1: 47–80.Google Scholar
  28. Montgomery, D. C. and Peck, E. A. (1982), Introduction to Linear Regression Analysis, New York: John Wiley & Sons.Google Scholar
  29. Nilsson, N. (1984), Shakey the Robot, Technical Note 323, Intelligence Center, SRI International, Menlo Park, CA.Google Scholar
  30. Nisbett, R. E., Krantz, D. H., Jepson, D., and Kunda, Z. (1983), ‘The use of statistical heuristics in everyday inductive reasoning’, Psychological Review 90: 339–363.CrossRefGoogle Scholar
  31. Rissland, E. L. and Ashley, K. D. (1986), ‘Hypotheticals as heuristic device’, in Proceedings of the National Conference on Artificial Intelligence (AAAI-86), Los Altos, CA: Morgan Kaufmann, pp. 289–297.Google Scholar
  32. Rosenbloom, P. S. and Newell, A. (1986), ‘The chunking of goal hierarchies: A generalized model of practice’, in Michalski, R. S., Carbonell, J. G. and Mitchell, T. M. (eds.), Machine Learning: An Artificial Intelligence Approach, Volume II. Los Altos, CA: Morgan Kaufmann, pp. 247–288.Google Scholar
  33. Russell, S. J. (1986), Analogical and Inductive Inference, PhD Thesis, Stanford University, Stanford CA.Google Scholar
  34. Russell, S. J. and Grosof, B. N. (1987), ‘A declarative approach to bias in inductive concept learning’, in Proceedings of the National Conference on Artificial Intelligence (AAAI-87), Los Altos, CA: Morgan Kaufmann, pp. 505–510.Google Scholar
  35. Shaw, W. H. and Ashley, L. R. (1983), ‘Analogy and inference’, Dialogue: Canadian Journal of Philosophy 22: 415–432.CrossRefGoogle Scholar
  36. Subramanian, D. and Genesereth, M. R. (1987), ‘The relevance of irrelevance’, in Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87), Los Altos, CA: Morgan Kaufmann, pp. 416–422.Google Scholar
  37. Thagard, P. and Nisbett, R. E. (1982), ‘Variability and confirmation’, Philosophical Studies 42, 379–394.CrossRefGoogle Scholar
  38. Theil, H. (1970), ‘On the estimation of relationships involving qualitative variables’, American Journal of Sociology 76: 103–154.CrossRefGoogle Scholar
  39. Ullman, J. D. (1983), Principles of Database Systems, Rockville, MD: Computer Science Press.Google Scholar
  40. Vardi, M. Y. (1982), The Implication and Finite Implication Problems for Typed Template Dependencies, Technical Report STAN-CS-82–912, Stanford University, Stanford, CA.Google Scholar
  41. Weitzenfeld, J. S. (1984), ‘Valid reasoning by analogy’, Philosophy of Science 51: 137–149.CrossRefGoogle Scholar
  42. Wilson, P. R. (1964), ‘On the argument by analogy’, Philosophy of Science 31: 34–39.CrossRefGoogle Scholar
  43. Winston, P. H. (1980) ‘Learning and reasoning by analogy’, Communications of the Association for Computing Machinery 23: 689–703.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1988

Authors and Affiliations

  • Todd R. Davies
    • 1
  1. 1.Artificial Intelligence Center, SRI International and Department of PsychologyStanford UniversityUSA

Personalised recommendations