Mathematics Flagship


O. Caprotti, J. Saludes
Universitat Politècnica de Catalunya

MOLTO review
2013-05-22

Presenter Notes

The Mathematical Grammar Library

Contributors: Jordi Saludes, Ares Ribó, Sebastian Xambó, Olga Caprotti, Aarne Ranta, Krasimir Angelov, Ramona Enach, Adam Slaski, Thomas Hallgren, Shafqat Mumtaz Virk

The goal of the MGL is to provide mathematics in natural language in many natural languages, including interfacing with software.

Presenter Notes

High-quality multilingual mathematics

  • Preserving meaning essential
  • Based on the OpenMath standard.
  • Mixing formulas and natural language.
  • Supporting numbers, functions, sets, vectors and matrices.
  • More than 12 languages available.
  • Aimed at encoding exercises for freshmen Linear Algebra and Calculus.

Presenter Notes

Use cases

  • Used in gfsage (see the Query Technologies Flagship)
  • MathTalk

Presenter Notes

Historical development

  • It started with EU project webALT.

    • Goal: To have a repository of multilingual mathematical exercises in high school Algebra and Calculus

    • First contact with GF

    • RGL and language not mature enough

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Design and Modularity

The library is organized in three layers of increasing complexity:

  • Ground layer : contains basic and atomic elements. Modules Ground and Variables.
  • OpenMath layer: the bulk of the library resides here, a module for each targeted OpenMath Content Dictionary.
  • Operations layer: for expressing simple mathematical drills by combining an imperative (Compute, Prove, Find, etc.) with the productions of the OpenMath layer.

Presenter Notes

Expressivity

Mathematics as done using OpenMath, a language especially designed for the online representation and communication of meaningful mathematical expressions electronically. It is also possible to express a sequence of simple computations as done in gfsage, or mathematical problems, as done in MathTalk and in the Word Problems.

Presenter Notes

Modularity of the MGL

The abstract modular structure of the MGL in the case of quantification and variables.

Presenter Notes

these are just to show the complexity of the modular structure

Quantification and Variables in English