Skip to main content
SpringerLink
Log in

Genetic Reasoning: Evolutionary Induction of Mathematical Proofs

  • Conference paper
  • First Online:
Book cover Genetic Programming (EuroGP 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1598))

Included in the following conference series:

Abstract

Most automated reasoning systems rely on human knowledge or heuristics to guide the reasoning or search for proofs. We have evaluated the use of a powerful general search algorithm to search in the space of mathematical proofs. In our approach, automated reasoning is seen as an instance of automated programming where the proof is seen as a program (of functions corresponding to rules of inference) which transforms a statement into an axiom. We use genetic programming as the general technique for automated programming. We show that such a system can be used to evolve mathematical proofs in complex domains, i.e. arithmetics. We extend our previous research by the implementation of an efficient and stable C-language system in contrast to earlier work in Prolog.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Banzhaf, W., Nordin, P., Keller R.E., Francone, F.D. (1998) Genetic Programming-An Introduction. Morgan Kauffmann, San Fransisco, and d-punkt, Heidelberg, Germany.

    Book  MATH  Google Scholar 

  2. Bledsoe W. W., (1977) Non-Resolution Theorem Proving, In Artificial Intelligence, Vol. 9, pp 2–3.

    Article  MathSciNet  MATH  Google Scholar 

  3. Boyer R.S., Moore J.S. (1979) Proving Teorems about LISP-Functions, In J.ACM, Vol. 22, pp 129–144.

    Article  MATH  Google Scholar 

  4. Boyer R.S., Yu Y. (1992) Automated Correctness Proofs of Machine Code Programs for a Commercial Microprocessor, In Automated Deduction-CADE-11 Kapur D. (Ed), pp. 416–430.

    Google Scholar 

  5. Bundy A., (1983) The Computer Modeling of Mathematical Reasoning, Academic Press, London, pp. 74–77.

    MATH  Google Scholar 

  6. James W. (1890) The principles of psychology Vol.1. Originally published: Henry Holt, New York 1890.

    Book  Google Scholar 

  7. Koza, J. (1992) Genetic Programming, MIT Press, Cambridge, MA

    MATH  Google Scholar 

  8. Lowerre, B.T., Reddy, R.D. (1980) The Harpy Speech Understanding System. In Trends in Speech Recognition. Lea, W.A. (Ed.) Englewood Cliffs, Prentice-Hall, New York.

    Google Scholar 

  9. McCune W.W. (1994) Otter 3.0 Reference Manual and Guide. Argonne National Laboratory, Argonne, USA.

    Book  Google Scholar 

  10. Newell, A., Shaw J.C., and Simon H. (1957) Empirical Explorations of the Logic Theorem Machine: A case study in Heuristic, in Proceedings of Western Joint Computer Conference Vol. 15.

    Google Scholar 

  11. Nordin J.P., Banzhaf W. (1995a) Complexity Compression and Evolution, in Proceedings of Sixth International Conference of Genetic Algorithms, Pittsburgh, 995, L. Eshelman (ed.), Morgan Kaufmann, San Mateo, CA

    Google Scholar 

  12. Nordin, J.P.,F. Francone, Banzhaf W. (1995b) Explicitly Defined Introns in Genetic Programming. In Advances in Genetic Programming II, (In press) Kim Kinnear, Peter Angeline (Eds.), MIT Press USA.

    Google Scholar 

  13. Nordin, J.P., Banzhaf W.(1995c) Controlling an Autonomous Robot with Genetic Programming. In proceedings of: 1996 AAAI fall symposium on Genetic Programming, Cambridge, USA.

    Google Scholar 

  14. Robinson J.A., (1965) A Machine Oriented Logic Based on the Resolution Principle, In J.ACM, Vol. 12, No. 1, pp. 23–41.

    Article  MathSciNet  MATH  Google Scholar 

  15. Rosenblom, P. (1987) Best First Search. In Encyclopedia of Artificial Intelligence, Shapiro, S. (Ed) Vol. 2, Wiley, New York.

    Google Scholar 

  16. Russel S., Norvig P. (1995) Artificial Intelligence: A modern approach. Prentice-Hall, Inc.

    Google Scholar 

  17. Winker S., Wos L., (1978) Automated Generation of Models and Counterexamples and its application to Open Questions in Ternary Boolean Algebra, In Proceedings of 8th international symposium Multiple-Valued Logic, Rosemont, Ill., IEEE and ACM, pp. 251–256, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physical Resource Theory, Chalmers University of Technology, S-41296, Göteborg, Sweden

    Peter Nordin, Anders Eriksson & Mats Nordahl

Authors
  1. Peter Nordin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anders Eriksson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mats Nordahl
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Egdbaston, Birmingham, B15 2TT, UK

    Riccardo Poli

  2. Department of Physical Resource Theory, Chalmers University of Technology, S-412 96, Göteborg, Sweden

    Peter Nordin

  3. Centrum voorWiskunde en Informatic, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    William B. Langdon

  4. Napier University, 219 Colinton Road, Edinburgh, EH14 1DJ, UK

    Terence C. Fogarty

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nordin, P., Eriksson, A., Nordahl, M. (1999). Genetic Reasoning: Evolutionary Induction of Mathematical Proofs. In: Poli, R., Nordin, P., Langdon, W.B., Fogarty, T.C. (eds) Genetic Programming. EuroGP 1999. Lecture Notes in Computer Science, vol 1598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48885-5_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-48885-5_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65899-3

  • Online ISBN: 978-3-540-48885-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation