Skip to main content

Translating Mizar for First Order Theorem Provers

  • Conference paper
  • First Online:
Mathematical Knowledge Management (MKM 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2594))

Included in the following conference series:

Abstract

The constructor system of the Mizar proof checking system is explained here on examples from Mizar articles,and its translation to untyped first-order syntax is described and discussed.This makes the currently largest library of formalized mathematics available to first- order theorem provers.

A more detailed version of this article will be a part of author’s PhD thesis.

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. Johan Belinfante, On a Modification of Godel’s Algorithm for Class Formation, Association for Automated Reasoning Newsletter, No.34,pp.1015 (1996)]

    Google Scholar 

  2. Bonarska, E., An Introduction to PC Mizar, Fondation Ph.le Hodey, Brussels,1990.

    Google Scholar 

  3. Ingo Dahn. Interpretation of a Mizar-like Logic in First Order Logic. Proceedings of FTP 1998.pp.137–151.

    Google Scholar 

  4. J. Goguen and J. Meseguer. Order-sorted algebra I:Equational deduction formultiple inheritance,overloading,exceptions and partial operations. Theoretical Computer Science, 105(2): 217–273, 1992.

    Article  MathSciNet  Google Scholar 

  5. R. Hahnle, M. Kerber, and C. Weidenbach. Common Syntax of the DFGSchwerpunktprogramm Deduction.Technical Report TR 10/96, Fakultät für Informatik,Universät Karlsruhe, Karlsruhe, Germany,1996.

    Google Scholar 

  6. McCune, W. W., OTTER 3.0 Reference Manual and Guide, Technical Report ANL-94/6, Argonne National Laboratory, Argonne, Illinois (1994).

    Google Scholar 

  7. Muzalewski, M., An Outline of PC Mizar, Fondation Philippe le Hodey, Brussels, 1993.

    Google Scholar 

  8. 1]_Krzysztof Hryniewiecki, Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.

    Google Scholar 

  9. Rudnicki, P., An Overview of the Mizar Project, Proceedings of the 1992 Workshop on Types for Proofs and Programs, Chalmers University of Technology, Bastad, 1992.

    Google Scholar 

  10. J. M. Schumann, Automated Theorem-Proving in Software Engineering. Springer-Verlag, 2001.

    Google Scholar 

  11. C. Suttner and G. Sutcliffe. The TPTP problem library (TPTP v2.2.0). Technical Report 9704, Department of Computer Science, James Cook University, Townsville, Australia,1998.

    Google Scholar 

  12. Weidenbach C., Afshordel B., Brahm U., Cohrs C., Engel T., Keen R., Theobalt C.and Topic D., System description:Spass version 1.0.0, in H. Ganzinger, ed., ‘16th International Conference on Automated Deduction,CADE-16”, Vol. 1632 of LNAI, Springer, pp 314–318

    Google Scholar 

  13. Freek Wiedijk. Mizar:An impression. Unpublished paper,1999. http://www.cs.kun.nl/~freek/mizar/mizarintro.ps.gz.

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Urban, J. (2003). Translating Mizar for First Order Theorem Provers. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds) Mathematical Knowledge Management. MKM 2003. Lecture Notes in Computer Science, vol 2594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36469-2_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-36469-2_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00568-1

  • Online ISBN: 978-3-540-36469-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics