Skip to main content

XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy

  • Conference paper
Mathematical Knowledge Management (MKM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3863))

Included in the following conference series:

Abstract

Since version 7.2 the Mizar system produces quite detailed XML-based semantic description of Mizar articles during their verification. This format is now used natively for most of the processing done by Mizar, e.g., also for the whole Mizar internal database. The main motivation for switching to this XML-based representation is to make semantic communication with Mizar and presentation of the MML more accessible to a variety of external tools and systems. This article briefly describes this format and its current implementation, and shows examples of its usage. These examples include presentation of linked Mizar articles in modern XML-capable browsers like Mozilla, authoring assistance in the Mizar mode for Emacs, and experiments with XML-based querying languages like XQuery over the Mizar Mathematical Library loaded into a native XML databases like eXist. This work makes the currently largest repository of formal mathematics available to many kinds of presentational, data-mining, and automated reasoning applications and experiments, and the goal of this article is also to encourage, facilitate and provide recipes for the development of such applications.

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. Bancerek, G., Rudnicki, P.: Information retrieval in MML. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 119–132. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Bancerek, G., Urban, J.: Integrated semantic browsing of the Mizar Mathematical Library for authoring Mizar articles. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 44–57. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Carlson, A.J., Cumby, C.M., Rosen, J.L., Roth, D.: Snow user’s guide. Technical Report UIUC-DCS-R-99-210, UIUC (1999)

    Google Scholar 

  4. Dahn, I.: Interpretation of a Mizar-like logic in first-order logic. In: Caferra, R., Salzer, G. (eds.) FTP 1998. LNCS (LNAI), vol. 1761, pp. 137–151. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Jaskowski, S.: On the rules of suppositions. Studia Logica 1 (1934)

    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. Meier, W.: eXist: An open source native XML database. In: Chaudhri, A.B., Jeckle, M., Rahm, E., Unland, R. (eds.) NODe-WS 2002. LNCS, vol. 2593, pp. 169–183. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Matuszewski, R., Rudnicki, P.: Mizar: the first 30 years. In: Bancerek, G. (ed.) MKM Workshop on 30 Years of Mizar (2004)

    Google Scholar 

  9. Pelletier, F.J.: A brief history of natural deduction. History and Philosophy of Logic 20, 1–31 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ramakrishnan, I.V., Sekar, R., Voronkov, A.: Handbook of Automated Reasoning, chapter Term Indexing, pp. 1853–1964. Elsevier/MIT Press (2001)

    Google Scholar 

  11. Rudnicki, P., Trybulec, A.: On equivalents of well-foundedness. J. Autom. Reasoning 23(3-4), 197–234 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Rudnicki, P.: An overview of the Mizar project. In: 1992 Workshop on Types for Proofs and Programs, Chalmers University of Technology, Bastad, pp. 311–332 (1992)

    Google Scholar 

  13. Urban, J.: MPTP - motivation, implementation, first experiments. Journal of Automated Reasoning 33(3-4), 319–339 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Urban, J.: MizarMode - an integrated proof assistance tool for the Mizar way of formalizing mathematics. Journal of Applied Logic (2005), forthcoming, available online at http://ktiml.mff.cuni.cz/~urban/mizmode.ps

  15. Urban, J.: MoMM - fast interreduction and retrieval in large libraries of formalized mathematics. International Journal on Artificial Intelligence Tools (2005), forthcoming, available online at http://ktiml.mff.cuni.cz/~urban/MoMM/momm.ps

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Urban, J. (2006). XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy. In: Kohlhase, M. (eds) Mathematical Knowledge Management. MKM 2005. Lecture Notes in Computer Science(), vol 3863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11618027_23

Download citation

  • DOI: https://doi.org/10.1007/11618027_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31430-1

  • Online ISBN: 978-3-540-31431-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics