Skip to main content
SpringerLink
Log in

Extracting Mathematical Semantics from \({L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}\) Documents

  • Conference paper
Principles and Practice of Semantic Web Reasoning (PPSWR 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2901))

Abstract

We report on a project to use SGLR parsing and term rewriting with ELAN4 to extract the semantics of mathematical formulas from a \({L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}\) document and representing them in MathML. The \({L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}\) document we used is part of the Digital Library of Mathematical Functions (DLMF) project of the US National Institute of Standards and Technology (NIST) and obeys project-specific conventions, which contains macros for mathematical constructions, among them 200 predefined macros for special functions, the subject matter of the project. The SGLR parser can parse general context-free languages, which suffices to extract the structure of mathematical formulas from calculus that are written in the usual mathematical style, with most parentheses and multiplication signs omitted. The parse tree is then rewritten into a more concise and uniform internal syntax that is used as the base for extracting MathML or other semantical information.

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

Access this chapter

Log in via an institution
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. Abramowitz, M., Stegun, I. (eds.): Handbook of Mathematical Functions. National Bureau of Standards, USA (1964)

    MATH  Google Scholar 

  2. Aigner, M., Ziegler, G.M.: Proofs from THE BOOK. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  3. Borovanský, P., Cirstea, H., Dubois, H., Kirchner, C., Kirchner, H., Moreau, P.-E., Ringeissen, C., Vittek, M.: ELAN V 3.3 User Manual, 3rd edn., LORIA, Nancy (France) (December 1998)

    Google Scholar 

  4. van den Brand, M.G.J., Scheerder, J., Vinju, J.J., Visser, E.: Disambiguation Filters for Scannerless Generalized LR Parsers. In: Horspool, R.N. (ed.) CC 2002. LNCS, vol. 2304, pp. 143–158. Springer, Heidelberg (2002), See http://www.cwi.nl/projects/MetaEnv/

    Chapter  Google Scholar 

  5. Bronstein, I.N., Semendjajew, K.A., Musiol, G., Mühlig, H.: Taschenbuch der Mathematik, 5th edn., Harri Deutsch (2000)

    Google Scholar 

  6. Carlisle, D., Ion, P., Miner, R., Poppelier, N.: Mathematical Markup Language (MathML) Version 2.0. W3C, February 21 (2001), http://www.w3.org/TR/2001/REC-MathML2-20010221/

  7. van Deursen, A., Heering, J., Klint, P. (eds.): Language Prototyping: An Algebraic Specification Approach. AMAST Series in Computing, vol. 5. World Scientific, Singapore (1996)

    MATH  Google Scholar 

  8. Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics, 2nd edn. Addison-Wesley, Reading (1994)

    MATH  Google Scholar 

  9. Gurari, E.M.: Tex4ht: Latex and tex for hypertext, http://www.cis.ohio-state.edu/~gurari/TeX4ht/mn.html

  10. Kohlhase, M.: OMDoc: An open markup format for mathematical documents (2003), See http://www.mathweb.org/omdoc/

  11. Kuipers, T., Visser, J.: Object-oriented tree traversal with JJForester. Science of Computer Programming 47(1), 59–87 (2002)

    Article  Google Scholar 

  12. Lang, S.: Algebra, 3rd edn. Addison-Wesley, Reading (1993)

    MATH  Google Scholar 

  13. Moonen, L.: Generating robust parsers using island grammars. In: Proc. 8th Working Conf. on Reverse Engineering, pp. 13–22. IEEE Computer Society Press, Los Alamitos (2001)

    Chapter  Google Scholar 

  14. Moreau, P.-E., Ringeissen, C., Vittek, M.: A Pattern Matching Compiler for Multiple Target Languages. In: Hedin, G. (ed.) CC 2003. LNCS, vol. 2622, pp. 61–76. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Olver, F.W.J.: Digital Library of Mathematical Functions, chapter Airy and Related Functions. National Institute of Standards and Technology (2001), http://dlmf.nist.gov/Contents/AI/index.html

  16. OpenMath, http://www.openmath.org/

  17. Plaice, J., Haralambous, Y.: Produire du MathML et autres.. ML à partir d’Ω: Ω se généralise. In: Cahiers GUTenberg no 33 — actes du congrès GUT 1999, Lyon (May 1999)

    Google Scholar 

  18. Scheja, G., Storch, U.: Lehrbuch der Algebra, 2nd edn. B.G. Teubner, Stuttgart (1994)

    Google Scholar 

  19. van den Brand, M.G.J., de Jong, H.A., Klint, P., Olivier, P.A.: Efficient annotated terms. Software, Practice and Experience 30(3), 259–291 (2000)

    Article  Google Scholar 

  20. Wolfram, S.: Mathematical notation: Past and future. Transcript of a keynote address presented at MathML and Math on the Web: MathML International Conference (2000), Available at http://www.stephenwolfram.com/publications/talks/mathml/

Download references

Author information

Authors and Affiliations

  1. LORIA École des Mines de Nancy, 615 Rue du Jardin Botanique, 54600, Villers-lès-Nancy, France

    Jürgen Stuber

  2. Department of Software Engineering, Centrum voor Wiskunde en Informatica, Kruislaan 413, NL-1098 SJ, Amsterdam, The Netherlands

    Mark van den Brand

  3. Instituut voor Informatica en Electrotechniek, Hogeschool van Amsterdam, Weesperzijde 190, NL-1097 DZ, Amsterdam, The Netherlands

    Mark van den Brand

Authors
  1. Jürgen Stuber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark van den Brand
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Informatics, University of Munich, Oettingenstr. 67, D-80538, München, Germany

    François Bry

  2. IVS - Semantic Web Group, Leibniz University of Hannover, Appelstr. 4, D-30167, Hannover, Germany

    Nicola Henze

  3. Department of Computer and Information Science, Linköping University, 581 83, Linköping, Sweden

    Jan Małuszyński

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stuber, J., van den Brand, M. (2003). Extracting Mathematical Semantics from \({L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}\) Documents. In: Bry, F., Henze, N., Małuszyński, J. (eds) Principles and Practice of Semantic Web Reasoning. PPSWR 2003. Lecture Notes in Computer Science, vol 2901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24572-8_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24572-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20582-1

  • Online ISBN: 978-3-540-24572-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation