Skip to main content

Tentative Experiments with Ellipsis in Mizar

  • Conference paper
Intelligent Computer Mathematics (CICM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7362))

Included in the following conference series:

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.

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. Mizar homepage, http://mizar.org/

  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)

    MATH  Google Scholar 

  3. Bancerek, G.: The fundamental properties of natural numbers. Formalized Mathematics 1(1), 41–46 (1990)

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. Łukaszewicz, L.: Triple dots in a formal language. Journal of Automated Reasoning 22, 223–239 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  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. Fitch, F.B.: Symbolic logic, an introduction. Ronald Press Co., New York (1952)

    MATH  Google Scholar 

  10. Ono, K.: On a practical way of describing formal deductions. Nagoya Mathematical Journal 21, 115–121 (1962)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Korniłowicz, A. (2012). Tentative Experiments with Ellipsis in Mizar. In: Jeuring, J., et al. Intelligent Computer Mathematics. CICM 2012. Lecture Notes in Computer Science(), vol 7362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31374-5_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31374-5_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31373-8

  • Online ISBN: 978-3-642-31374-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics