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A grammar-based approach to multilingual mathematics


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In this talk we present the current state of the art of the Mathematical Grammar Library, a software library for the GF system, that allows to render mathematics in many natural languages while maintaining the underlying semantics of the expression. The work is being done in the EU project MOLTO.

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A grammar-based approach to multilingual mathematics

  1. 1. A grammar-based approachto multilingual mathematicsJordi Saludes, Olga Caprotti, Sebastian Xambó-DescampsUPC, Barcelona5th International Workshop on Mathematical e-Learning, 4-5 April 2013. UNED, Madrid (Spain).1Monday, April 8, 13
  2. 2. Non multa, sed multumMOLTO - Multilingual Online Translation❖ 36+3 months❖ start:1/3/2010❖ start EEU: 1/1/2012❖ end: 31/5/2013❖ 2.395000+ 600000 €2Monday, April 8, 13
  3. 3. MOLTO-EEUa larger Consortium❖ approved on 7/12/2011❖ 2 new countries/languages:❖ Be Informed (NL)❖ Uni Zürich (CH)❖ 2 new use cases:❖ decision making system❖ multilingual semanticwikis3Monday, April 8, 13
  4. 4. Quick listAll deliverables (not updated), April 8, 13
  5. 5. Any language, whether formal or natural, is thebasic tool for reasoning and communicating(with a fellow or a machine) along time andacross spaceAlong time: archival publicationsAcross space: crossing borders (mental borders too :),disciplines or mental frameworks)Multilingual, natural, mathematical languageUse case: Mathematics5Monday, April 8, 13
  6. 6. Thinking, speaking and writingare core competenciesA professional thinks, speaks, and writes in aspecialized language, the level of expertise iso3en noticed by the kind of languageemployed.from the point of view of language learningEducation6Monday, April 8, 13
  7. 7. A QUESTION TO THE EDUCATORSLately we seem to pay no effort to translating:foreign jargon abounds.WHY?global marketwhat aboutlocal communities of practice?new areas of research and development?7Monday, April 8, 13
  8. 8. Naming abstract objectsand proving statementsabout them is the job of amathematician.A mathematician compilesa dictionary in his/her areaof research.Symbolic lexicographersMathematicians are lexicographers, too8Monday, April 8, 13
  9. 9. CLAIM:Some notation we commonly use is o3en remnantof the original definitionLet K be a field - where K is short for KörperQ, the set of Rationals - Q for “quoziente” (Peano)Z, the set of Integers - for Zahlen( math notationInklings of translations9Monday, April 8, 13
  10. 10. The set of fractions QDie Menge der Brücke Q10Monday, April 8, 13
  11. 11. WebALT - Web Advanced Learning Technologies (EDC-22253, 2005-2008)Yet it is multilingualMathematics is universalFirst release of a Mathematical Grammar Library based on GF11Monday, April 8, 13
  12. 12. Jordi Saludes will demonstrate✴ online mathematical translator✴ word problem tutorMathematical Grammar LibraryDemo12Monday, April 8, 13