Skip to main content

A sketch of analogy as reasoning with equality hypotheses

  • Submitted Papers
  • Conference paper
  • First Online:
Analogical and Inductive Inference (AII 1989)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 397))

Included in the following conference series:

Abstract

We specify a form of analogical reasoning in terms of a system of hypothetical reasoning based on mathematical logic. Our primary motivation is a deeper understanding of analogical reasoning as well as its relationship to existing logical models of nonmonotonic reasoning.

We begin with a brief description of a hypothetical reasoning system called Theorist. Theorist is a nonmonotonic clausal theorem prover that permits consistent instances of hypotheses to participate in a deductive derivation. Such sets are viewed as explanatory theories for goal observations, which are simply questions assumed true in the intended interpretation.

Our specification of analogical reasoning assumes two relatively simple and uncontroversial properties of analogical reasoning. First, analogical reasoning is non-deductive. Second, analogical reasoning is based on similarity relationships between so-called source and target objects. We use Theorist's specification of hypothetical reasoning to provide us with the required non-deductive mechanism, and interpret similarity relationships as hypotheses about various kinds of equality between source and target objects.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. S.E. August and M.G. Dyer. Analogy recognition and comprehension in editorials. Technical report, Computer Science Department, University of California at Los Angeles, Los Angeles, California, April 1986.

    Google Scholar 

  2. M.H. Burnstein. Concept formation by incremental analogical reasoning and debugging. In R. Michalski, J.G. Carbonell, and T.M. Mitchell, editors, Machine Learning, volume II, pages 351–369. Morgan Kaufmann, Los Altos, Ca., 1986.

    Google Scholar 

  3. K.L. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and Databases, pages 293–322. Plenum Press, New York, 1978.

    Google Scholar 

  4. R.P. Daley. Twards the development of an analysis of learning algorithms. In K.P. Jantke, editor, Analogical and Inductive Inference, volume 265 of Lecture Notes in Computer Science, pages 1–18. Springer-Verlag, New York, 1987.

    Google Scholar 

  5. T.R. Davies and S.J. Russell. A logical approach to reasoning by analogy. In Proceedings of IJCAI-87, pages 264–270, Milan, Italy, August 23–28 1987.

    Google Scholar 

  6. J.J. Finger. Residue: a deductive approach to synthesis. Technical Report STAN-CS-85-1035, Department of Computer Science, Stanford University, Stanford, California, 1985.

    Google Scholar 

  7. R. Goebel and S.D. Goodwin. Applying theory formation to the planning problem. In Proceedings of the AAAI Workshop on The Frame Problem in Artificial Intelligence, pages 207–232, Lawrence, Kansas, April 12–15 1987.

    Google Scholar 

  8. R. Greiner. Learning by understanding analogies. Artificial Intelligence, 35(1):81–125, 1988.

    Google Scholar 

  9. M. Haraguchi and S. Arikawa. Reasoning by Analogy as a Partial Identity between Models. In K.P. Jantke, editor, Analogical and Inductive Inference, volume 265 of Lecture Notes in Computer Science, pages 61–87. Springer-Verlag, New York, 1987.

    Google Scholar 

  10. R.P. Hall. Computational approaches to analogical reasoning: A comparative analysis. Artificial Intelligence, 39(1):39–120, 1989.

    Google Scholar 

  11. D.R. Hofstadter and M. Mitchell. Concepts, analogies, and creativity. In Proceedings of CSCSI-88, pages 94–101, Edmonton, Alberta, June 6–10 1988.

    Google Scholar 

  12. D.J. Israel. What's wrong with non-monotonic logic? In Proceedings of AAAI-80, pages 99–101, Stanford, California, August 18–21 1980. Stanford University.

    Google Scholar 

  13. D.J. Israel. The role of logic in knowledge representation. Computer, 16(10):37–41, 1983.

    Google Scholar 

  14. D.J. Israel. On cheeseman. Computational Intelligence, 4(1):85–86, 1988.

    Google Scholar 

  15. K.P. Jantke, editor. Analogical and Inductive Inference, volume 265 of Lecture Notes in Computer Science. Springer-Verlag, New York, 1987.

    Google Scholar 

  16. S.T. Kedar-Cabelli. Analogy — From a Unified Perspective. Technical report, Laboratory for Computer Science Research, Rutgers University, New Brunswick, New Jersey, December 1985.

    Google Scholar 

  17. H. Levesque (ed.). Taking issue: Mcdermott's a critique of pure reason. Computational Intelligence, 3(3), 1987.

    Google Scholar 

  18. J.W. Lloyd and M.H. van Emden. A logical reconstruction of Prolog ii. In Proceedings of the Second International Logic Programming Conference, pages 115–125, Uppsala, Sweden, July 2–6 1984. Uppsala University.

    Google Scholar 

  19. D.V. McDermott. A critique of pure reason. Computational Intelligence, 3(3):151–160, 1987.

    Google Scholar 

  20. Ch. Melis and Melis E. Some considerations about formalization of analogical reasoning. In K.P. Jantke, editor, Analogical and Inductive Inference, volume 265 of Lecture Notes in Computer Science, pages 125–134. Springer-Verlag, New York, 1987.

    Google Scholar 

  21. M. McLeish (ed.). Taking issue: Cheeseman's an inquiry into computer understanding. Computational Intelligence, 4(1):57–142, 1988.

    Google Scholar 

  22. L.T. McCarty and N.S. Sridharan. A computational theory of legal argument. Laboratory for Computer Science Technical Report LRP-TR-13, Department of Computer Science, Rutgers University, New Brunswick, New Jersey, November 1981.

    Google Scholar 

  23. D. Poole, R. Goebel, and R. Aleliunas. Theorist: A logical reasoning system for defaults and diagnosis. In N.J. Cercone and G. McCalla, editors, The Knowledge Frontier: Essays in the Representation of Knowledge, pages 331–352. Springer Verlag, New York, 1987.

    Google Scholar 

  24. G. Polya. How to Solve It: A New Aspect of Mathematical Method. Princeton University Press, Princeton, New Jersey, second, 1957 edition, 1954.

    Google Scholar 

  25. D.L. Poole. Variables in hypotheses. In Proceedings of IJCAI-87, pages 905–908, Milan, Italy, August 23–28 1987.

    Google Scholar 

  26. D. Poole. A logical framework for default reasoning. Artifical Intelligence, 36(1):27–47, 1988.

    Google Scholar 

  27. R. Reiter. A logic for default reasoning. Artificial Intelligence, 13(1&2):81–132, 1980.

    Google Scholar 

  28. R. Reiter. Nonmonotonic reasoning. In Annual Reviews of Computer Science, pages 147–186. Annual Reviews of Computer Science, New York, 1987.

    Google Scholar 

  29. R. Reiter. A theory of diagnosis from first principles. Artificial Intelligence, 32(1):57–95, 1987.

    Google Scholar 

  30. P.H. Winston. Learning and Reasoning by Analogy. ACM Communications, 23(12):689–703, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Klaus P. Jantke

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Goebel, R. (1989). A sketch of analogy as reasoning with equality hypotheses. In: Jantke, K.P. (eds) Analogical and Inductive Inference. AII 1989. Lecture Notes in Computer Science, vol 397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51734-0_65

Download citation

  • DOI: https://doi.org/10.1007/3-540-51734-0_65

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51734-4

  • Online ISBN: 978-3-540-46798-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics