Revisions as an Essential Tool to Maintain Mathematical Repositories

  • Adam Grabowski
  • Christoph Schwarzweller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4573)


One major goal of Mathematical Knowledge Management is building extensive repositories, in which the mathematical knowledge has been verified. It appears, however, that maintaining such a repository is as hard as building it – especially for an open collection with a large number of contributors. In this paper we argue that even careful reviewing of contributions cannot cope with the task of keeping a mathematical repository efficient and clearly arranged in the long term. We discuss reasons for revisions of mathematical repositories accomplished by the “core implementors” and illustrate our experiences with revisions of MML, the Mizar Mathematical Library.


Mathematical Knowledge Essential Tool Revision Process Proof Checker Mizar Mathematical Library 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions; National Bureau of Standards, Applied Mathematics Series No. 55, U.S. Government Printing Office, Washington, DC (1964), see also
  2. 2.
    Adams, A.A., Davenport, J.H.: Copyright issues for MKM. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 1–16. Springer, Heidelberg (2004)Google Scholar
  3. 3.
    Bancerek, G.: Information retrieval and rendering with MML Query. In: Borwein, J.M., Farmer, W.M. (eds.) MKM 2006. LNCS (LNAI), vol. 4108, pp. 65–80. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    de Bruijn, N.G.: The Mathematical Vernacular, A Language for Mathematics with typed sets. In: Dybjer, P., et al. (eds.) Proc. of the Workshop on Programming Languages, Marstrand, Sweden (1987)Google Scholar
  5. 5.
    Davenport, J.H.: MKM from book to computer: A case study. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 17–29. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Grabowski, A.: On the computer-assisted reasoning about rough sets. In: Dunin-Kȩplicz, B., et al. (ed.) Monitoring, Security, and Rescue Techniques in Multiagent Systems, Advances in Soft Computing, pp. 215–226. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Grabowski, A., Schwarzweller, Ch.: Rough Concept Analysis – theory development in the Mizar system. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 130–144. Springer, Heidelberg (2004)Google Scholar
  8. 8.
    Kamareddine, F., Nederpelt, R.: A Refinement of de Bruijn’s Formal Language of Mathematics. Journal of Logic, Language and Information 13(3), 287–340 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Matuszewski, R., Rudnicki, P.: Mizar: the first 30 years. Mechanized Mathematics and Its Applications 4(1), 3–24 (2005)Google Scholar
  10. 10.
    Miller, B.R., Youssef, A.: Technical aspects of the Digital Library of Mathematical Functions. Annals of Mathematics and Artificial Intelligence 38, 121–136 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    The Mizar Homepage,
  12. 12.
    Naumowicz, A., Byliński, Cz.: Improving Mizar texts with properties and requirements. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 190–301. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    PlanetMath web page,
  14. 14.
    Rudnicki, P., Trybulec, A.: Abian’s fixed point theorem. Formalized Mathematics 6(3), 335–338 (1997)Google Scholar
  15. 15.
    Rudnicki, P., Trybulec, A.: Mathematical Knowledge Management in Mizar. In: Buchberger, B., Caprotti, O. (eds.) Proc. of MKM 2001, Linz, Austria (2001)Google Scholar
  16. 16.
    Rudnicki, P., Trybulec, A.: On the integrity of a repository of formalized mathematics. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 162–174. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. 17.
    Sacerdoti, C.: From proof-asistants to distributed knowledge repositories: tips and pitfalls. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 30–44. Springer, Heidelberg (2003)Google Scholar
  18. 18.
    Urban, J.: MoMM – fast interreduction and retrieval in large libraries of formalized mathematics. International Journal on Artificial Intelligence Tools 15(1), 109–130 (2006)CrossRefGoogle Scholar
  19. 19.
    Wolfram Mathworld web page,

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Adam Grabowski
    • 1
  • Christoph Schwarzweller
    • 2
  1. 1.Institute of Mathematics, University of Białystok, ul. Akademicka 2, 15-267 BiałystokPoland
  2. 2.Department of Computer Science, University of Gdańsk, ul. Wita Stwosza 57, 80-952 GdańskPoland

Personalised recommendations