Using Formal Concept Analysis in Mathematical Discovery

  • Simon Colton
  • Daniel Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4573)


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.


Query Sequence Chromatic Number Formal Context Formal Concept Analysis Hasse Diagram 
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.


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  1. 1.
    Colton, S.: Refactorable numbers - a machine invention. Journal of Integer Sequences, 2 (1999)Google Scholar
  2. 2.
    Colton, S., Dennis, L.: The numberswithnames program. In: Proceedings of the Seventh AI and Maths Symposium (2002)Google Scholar
  3. 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. 4.
    Colton, S.: Automated Theory Formation in Pure Mathematics. Springer, Heidelberg (2002)Google Scholar
  5. 5.
    Fajtlowicz, S.: On conjectures of Graffiti. Discrete Mathematics 72, 23, 113–118 (1988)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Fajtlowicz, S.: The writing on the wall. Unpublished preprint (1999), available from
  7. 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. 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. 9.
    Ganter, B., Stumme, G., Wille, R. (eds.): Formal Concept Analysis. Foundations and Applications. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  10. 10.
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  11. 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)zbMATHMathSciNetGoogle Scholar
  12. 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. 13.
    Liquiere, M., Sallantin, J.: Structural machine learning with galois lattice and graphs. In: International Conference on Machine Learning (1998)Google Scholar
  14. 14.
    Mohamadali, N.: A rational reconstruction of Graffiti. Master’s thesis, Department of Computing, Imperial College, London (2003)Google Scholar
  15. 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. 16.
    Schwarzweller, C.: Mizar formalization of concept lattices. Mechanized Mathematics and its Application 1(1), 1–10 (2000)Google Scholar
  17. 17.
    Sloane, N.J.A.: My favorite integer sequences. In: Proceedings of the International Conference on Sequences and Applications (1998)Google Scholar
  18. 18.
    Waterloo Maple. Maple Manual at,
  19. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Simon Colton
    • 1
  • Daniel Wagner
    • 1
  1. 1.Combined Reasoning Group, Department of Computing, Imperial College, London 

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