Skip to main content

Using Formal Concept Analysis in Mathematical Discovery

  • Conference paper
Towards Mechanized Mathematical Assistants (MKM 2007, Calculemus 2007)

Abstract

Formal concept analysis (FCA) comprises a set of powerful algorithms which can be used for data analysis and manipulation, and a set of visualisation tools which enable the discovery of meaningful relationships between attributes of the data. We explore the potential of combining FCA and mathematical discovery tools in order to better facilitate discovery tasks. In particular, we propose a novel lookup method for the Encyclopedia of Integer Sequences, and we show how conjectures from the Graffiti discovery program can be better understood using FCA visualisation tools. We argue that, not only can FCA tools greatly enhance the management and visualisation of mathematical knowledge, but they can also be used to drive exploratory processes.

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

Access this chapter

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. Colton, S.: Refactorable numbers - a machine invention. Journal of Integer Sequences, 2 (1999)

    Google Scholar 

  2. Colton, S., Dennis, L.: The numberswithnames program. In: Proceedings of the Seventh AI and Maths Symposium (2002)

    Google Scholar 

  3. Colton, S., Torres, P., Cairns, P., Sorge, V.: Managing automatically formed mathematical theories. In: Proceedings of the 5th International Conference on Mathematical Knowledge Management (2006)

    Google Scholar 

  4. Colton, S.: Automated Theory Formation in Pure Mathematics. Springer, Heidelberg (2002)

    Google Scholar 

  5. Fajtlowicz, S.: On conjectures of Graffiti. Discrete Mathematics 72, 23, 113–118 (1988)

    Article  MathSciNet  Google Scholar 

  6. Fajtlowicz, S.: The writing on the wall. Unpublished preprint (1999), available from http://math.uh.edu/~clarson/

  7. Ganter, B.: Formal Concept Analysis. Foundations and Applications. In: chapter Contextual Attribute Logic of Many-Valued Attributes, pp. 101–113. Springer, Heidelberg (2005)

    Google Scholar 

  8. Ganter, B., Kuznetsov, S.: Hypotheses and version spaces. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS, vol. 2746, pp. 83–95. Springer, Heidelberg (2003)

    Google Scholar 

  9. Ganter, B., Stumme, G., Wille, R. (eds.): Formal Concept Analysis. Foundations and Applications. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  10. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  11. Hidalgo, M., Martin-Mateos, F., Ruiz-Reina, J., Alonso, J.A., Borrego, J.: Verification of the Formal Concept Analysis. Rev. R. Acad. Cien. Serie A. Mat. 98(1), 3–16 (2004)

    MATH  MathSciNet  Google Scholar 

  12. Kuznetsov, S.: Machine learning and formal concept analysis. In: Eklund, P.W. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 287–312. Springer, Heidelberg (2004)

    Google Scholar 

  13. Liquiere, M., Sallantin, J.: Structural machine learning with galois lattice and graphs. In: International Conference on Machine Learning (1998)

    Google Scholar 

  14. Mohamadali, N.: A rational reconstruction of Graffiti. Master’s thesis, Department of Computing, Imperial College, London (2003)

    Google Scholar 

  15. Scheich, P., Skorsky, M., Vogt, F., Wachter, C., Wille, R.: Information and Classification - Concepts, Methods and Applications. In: chapter Conceptual Data Systems, pp. 72–84. Springer, Heidelberg (1992)

    Google Scholar 

  16. Schwarzweller, C.: Mizar formalization of concept lattices. Mechanized Mathematics and its Application 1(1), 1–10 (2000)

    Google Scholar 

  17. Sloane, N.J.A.: My favorite integer sequences. In: Proceedings of the International Conference on Sequences and Applications (1998)

    Google Scholar 

  18. Waterloo Maple. Maple Manual at, http://www.maplesoft.on.ca

  19. Yevtushenko, S.: System of data analysis concept explorer. In: Proceedings of the 7th national conference on Artificial Intelligence KII, pp. 127–134 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Manuel Kauers Manfred Kerber Robert Miner Wolfgang Windsteiger

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Colton, S., Wagner, D. (2007). Using Formal Concept Analysis in Mathematical Discovery . In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds) Towards Mechanized Mathematical Assistants. MKM Calculemus 2007 2007. Lecture Notes in Computer Science(), vol 4573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73086-6_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73086-6_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73083-5

  • Online ISBN: 978-3-540-73086-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics