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Tentative Experiments with Ellipsis in Mizar

  • Artur Korniłowicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7362)

Abstract

Ellipses are ubiquitous in mathematical texts. They allow writing sequences of terms or formulas in a concise way. In this paper, we show how ellipses are incorporated into the Mizar language and how they are verified by the Mizar proof checker.

Keywords

Inference Rule Formal Language Natural Deduction Mathematical Text 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.

References

  1. 1.
    Mizar homepage, http://mizar.org/
  2. 2.
    Grabowski, A., Korniłowicz, A., Naumowicz, A.: Mizar in a nutshell. Journal of Formalized Reasoning, Special Issue: User Tutorials I 3(2), 153–245 (2010)zbMATHGoogle Scholar
  3. 3.
    Bancerek, G.: The fundamental properties of natural numbers. Formalized Mathematics 1(1), 41–46 (1990)Google Scholar
  4. 4.
    Horozal, F., Kohlhase, M., Rabe, F.: Extending OpenMath with Sequences. In: Asperti, A., Davenport, J., Farmer, W., Rabe, F., Urban, J. (eds.) Intelligent Computer Mathematics, Work-in-Progress Proceedings, Volume UBLCS-2011-04 of Technical Report, University of Bologna, pp. 58–72 (2011)Google Scholar
  5. 5.
    Bundy, A., Richardson, J.: Proofs About Lists Using Ellipsis. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS (LNAI), vol. 1705, pp. 1–12. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Sexton, A.P., Sorge, V.: Abstract matrices in symbolic computation. In: Dumas, J.G. (ed.) International Symposium on Symbolic and Algebraic Computation (ISSAC), Genova, Italy, pp. 318–325. ACM Press (July 2006)Google Scholar
  7. 7.
    Łukaszewicz, L.: Triple dots in a formal language. Journal of Automated Reasoning 22, 223–239 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Jaśkowski, S.: On the rules of suppositions in formal logic. Studia logica. Nakładem Seminarjum Filozoficznego Wydziału Matematyczno-Przyrodniczego Uniwersytetu Warszawskiego (1934)Google Scholar
  9. 9.
    Fitch, F.B.: Symbolic logic, an introduction. Ronald Press Co., New York (1952)zbMATHGoogle Scholar
  10. 10.
    Ono, K.: On a practical way of describing formal deductions. Nagoya Mathematical Journal 21, 115–121 (1962)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Artur Korniłowicz
    • 1
  1. 1.Institute of InformaticsUniversity of BiałystokPoland

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