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Inductive equational reasoning

  • Machine Learning I
  • Conference paper
  • First Online:
PRICAI'96: Topics in Artificial Intelligence (PRICAI 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1114))

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Abstract

We present a simple learning algorithm for equational reasoning. The Knuth-Bendix algorithm can produce deductive consequences from sets of function equations but cannot deduce anything from grounded equations alone. This motivates an inductive procedure which conjectures function equations from a given database of grounded equations.

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References

  1. M. Bulmer. Reasoning by Term Rewriting. PhD thesis, University of Tasmania, 1995.

    Google Scholar 

  2. M. Bulmer. Inductive Theories from Equational Systems. Submitted for publication, 1996.

    Google Scholar 

  3. M. Bulmer, D. Fearnley-Sander, and T. Stokes. Towards a Calculus of Algorithms. Bulletin of the Australian Mathematical Society, 50(1):81–89, 1994.

    Google Scholar 

  4. L. J. Cohen. An Introduction to the Philosophy of Induction and Probability. Oxford University Press, 1989.

    Google Scholar 

  5. N. Dershowitz. Completion and its Applications. In H. Aït Kaci and M. Nivat, editors, Resolution of Equations in Algebraic Structures, volume 2, pages 31–85. Academic Press, London, 1989.

    Google Scholar 

  6. P. Gärdenfors. Knowledge in Flux: Modelling the Dynamics of Epistemic States. MIT Press, 1988.

    Google Scholar 

  7. G. Hinton. Learning Distributed Representations of Concepts. In L. Erlbaum, editor, Program of the Eight Annual Conference of the Cognitive Science Society. Amhearst, MA, 1986.

    Google Scholar 

  8. G. Huet. Cartesian Closed Categories and Lambda-Calculus. In G. Huet, editor, Logical Foundations of Functional Programming, pages 7–23. Addison-Wesley, Reading, Mass., 1990.

    Google Scholar 

  9. D. Kapur and D. R. Musser. Proof by Consistency. Artificial Intelligence, 31:125–157, 1987.

    Google Scholar 

  10. K. Popper. Conjectures and Refutations — The Growth of Scientific Knowledge. Routledge and Kegan Paul, London, 1974.

    Google Scholar 

  11. K. Popper. The Logic of Scientific Discovery. Hutchinson, London, 1974.

    Google Scholar 

  12. J. R. Quinlan. Learning Logical Definitions from Relations. Machine Learning, 5:239–266, 1990.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tasmania, GPO Box 252C, 7001, Hobart, Australia

    Michael Bulmer

Authors
  1. Michael Bulmer
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Editor information

Norman Foo Randy Goebel

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© 1996 Springer-Verlag Berlin Heidelberg

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Bulmer, M. (1996). Inductive equational reasoning. In: Foo, N., Goebel, R. (eds) PRICAI'96: Topics in Artificial Intelligence. PRICAI 1996. Lecture Notes in Computer Science, vol 1114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61532-6_2

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  • DOI: https://doi.org/10.1007/3-540-61532-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61532-3

  • Online ISBN: 978-3-540-68729-0

  • eBook Packages: Springer Book Archive

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