Skip to main content

Informalising Formal Mathematics: Searching the Mizar Library with Latent Semantics

  • Conference paper
Mathematical Knowledge Management (MKM 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3119))

Included in the following conference series:


Finding required information in a library of mathematics can be problematic, just as in any other library. However, so far, there are no strong search methods based on the semantics of formal mathematics. This paper describes a new approach based on latent semantic indexing (LSI). Using this, the semantics of terms need not be explicitly defined but is indirectly inferred from a body of documents in which the terms occur. The Mizar library is used as it is a substantial resource of formal mathematics. The system described in the paper adapts Mizar articles to produce an appropriate body of documents that can be used by LSI. Preliminary tests suggest that this approach is able to provide a useful mechanism for the search and retrieval of formal mathematics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Asperti, A., Buchberger, B., Davenport, J.H.: MKM 2003. LNCS, vol. 2594. Springer, Heidelberg (2003)

    Book  MATH  Google Scholar 

  2. Bancerek, G., Rudnicki, P.: Information Retrieval in MML. In: [1], pp. 119–132 (2003)

    Google Scholar 

  3. Bancerek, G.: Sequences of ordinal numbers. Formalized Mathematics 1(2), 281–290 (1990)

    Google Scholar 

  4. Bancerek, G.: Tarski’s classes and ranks. Formalized Mathematics 1(3), 563–567 (1990)

    Google Scholar 

  5. Baumgartner, P., Furbach, U.: Automated Deduction Techniques for the Management of Personalized Documents. Annals of Mathematics and Art. Intelligence 38, 211–288 (2003)

    Article  MATH  Google Scholar 

  6. Berry, M.W., Dumais, S.: Latent Semantic Indexing Web Site (accessed March 29, 2004),

  7. Byliński, C.: The modification of a function by a function and the iterations of the composition of a function. Formalized Mathematics 1(3), 521–527 (1990)

    Google Scholar 

  8. Cairns, P., Gow, J.: Using and parsing the Mizar language. Electronic Notes in Theoretical Computer Science, vol. 93, pp. 60–69. Elsevier, Amsterdam (2004)

    MATH  Google Scholar 

  9. Delahaye, D.: Information Retrieval in a Coq Proof Library Using Type Isomorphisms. In: Coquand, T., Nordström, B., Dybjer, P., Smith, J. (eds.) TYPES 1999. LNCS, vol. 1956, pp. 131–147. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. Giles, J.T., Wo, L., Berry, M.W.: GTP (General Text Parser) software for text mining. In: Bozdogan, H. (ed.) Statistical Data Mining and Knowledge Discovery, pp. 457–473. CRC Press, Boca Raton (2001)

    Google Scholar 

  11. Hryniewiecki, K.: Relations of tolerance. Formalized Mathematics 2(1), 105–109 (1991)

    Google Scholar 

  12. Java Compiler Compiler (accessed March 31, 2004),

  13. Karno, Z.: Remarks on special subsets of topological spaces. Formalized Mathematics 3(2), 297–303 (1992)

    Google Scholar 

  14. Korniłowicz, A.: The definition and basic properties of topological groups. Formalized Mathematics 7(2), 217–225 (1998)

    Google Scholar 

  15. Landauer, T.K., Foltz, P.W., Laham, D.: Introduction to latent semantic analysis. Discourse Processes 25, 259–284 (1998)

    Article  Google Scholar 

  16. Landauer, T.K.: LSA@Colorado University (accessed March 31, 2004),

  17. Miller, B.R., Youssef, A.: Technical aspects of the Digital Library of Mathematical Functions. Annals of Mathematics and Art. Intelligence 38, 121–136 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mirel, B.: Interaction Design for Complex Problem Solving. Morgan Kaufmann, San Francisco (2004)

    Google Scholar 

  19. Wysocki, M., Darmochwał, A.: Subsets of Topological Spaces. Formalized Mathematics 1(1), 231–237 (1990)

    Google Scholar 

  20. The Mizar Mathematical Library,

  21. Philips, L., Jørgensen, M.W.: Discourse Analysis as Theory and Method. Sage Publications, Thousand Oaks (2002)

    Book  Google Scholar 

  22. Rudnicki, P.: An overview of the Mizar project. In: Proceedings of 1992 Workshop on Types and Proofs for Programs (1992)

    Google Scholar 

  23. Text REtrieval Conference (TREC) (accessed March 31, 2004),

  24. Wiedijk, F.: Comparing Mathematical Provers. In: [1], pp. 188–202

    Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cairns, P. (2004). Informalising Formal Mathematics: Searching the Mizar Library with Latent Semantics. In: Asperti, A., Bancerek, G., Trybulec, A. (eds) Mathematical Knowledge Management. MKM 2004. Lecture Notes in Computer Science, vol 3119. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23029-8

  • Online ISBN: 978-3-540-27818-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics