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.

• 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.

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

• 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

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.

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.

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

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

Released with GPL at

svn co svn://molto-project.eu/tags/D6.1

constantly updated at

svn co svn://molto-project.eu/mgl

The MGL library consists on the following files and directories:

• One directory per language
• abstract directory: abstract modules of the library
• resources directory: the general resource modules, incomplete concrete modules and generic lexicon
• test: testing facilities and data

Contributors: Kaarel Kaljurand, Thomas Hallgren, Aarne Ranta, Jordi Saludes

The cloud services for mathematics provide linearization and parsing of mathematical text in many languages, as supported by the Mathematical Grammar Library.

• Math bar uses the GF standard JavaScript interface to an application grammar, in this case to the MGL.
• Multilingual semantic wiki on mathematics

Browser plugins and servies to deal with mathematical text, for instance to:

• translate the mathematical text,
• send it to a computational engine,
• prompt the user for some decision,
• explain some symbol,
• search in a mathematically meaningful way.

Contributors: Kaarel Kaljurand, Olga Caprotti, Jordi Saludes, Aarne Ranta, Ares Ribó

Demonstrate how to collaborative edit notes in mathematics, for instance to create online learning resources.

This special application grammar extends the MGL by constructs for stating mathematical problems and exercises, definitions and theorems. In particular it supports:

• Mixed formula/natural language rendering of mathematics.
• Usage of qualified variables in quantifiers:
  • for all prime natural numbers n and m, ...
• Work in progress.

Running on AceWiki-GF here.

Noteworthy features:

• A predictive parser allows a contributor to construct a well-formed statement or exercise.
• In English, Italian or Spanish.
• Automatically rendered in the reader language.
• A contributor is aware of ambiguous interpretations.

• Translations

• Ambiguities

  • Let x be a prime number. Then for all integer numbers y and z, if x divides the product of y and z then x divides y or x divides z.

  • It has 3 different meanings. The wiki shows the tree structure of all of them

    • 
    • 
    • 

• A command line tool for computing using natural language and aural replies.

  • Screencast for basic usage
  • Screencast showing feedback

• An embedded interface in the Sage notebook. Using natural language in a Sage cell by prefixing it with expressions like %english.

Contributors: Ares Ribó, Olga Caprotti, Thomas Hallgren, Aarne Ranta, Jordi Saludes

Assist a student into modeling word problems

• Tools for:

  • Writing a problem.

  • Screencast: Learning to model

• In the languages: English, Swedish, Spanish and Catalan.

• Classes and objects can be extended by adding entries to the WPEntities module.

We considered two levels of discourse:

• The plain language is for direct communication with the user, natural language;

• The core language is for the reasoner to work with.

Conjunctions are disaggregated: namely

• John has three apples and six bananas

is converted into:

• John has three apples
• John has six bananas

Make the unknown explicit in the core expressions:

• how many apples does Mary have?
• some apples

is denoted by a variable.

The authoring interpreter saves a word problem in a Prolog file consisting of:

• A GF abstract tree for the plain sentence of a problem. This is written as a Prolog comment.

• Core statements in Prolog format that correspond to the plain expression.

To process a given word problem, the student must construct a set of of statements in that model that given word problem.

When the dialog interpreter is started on a word problem file, the system uses the GF abstract lines to display the statement of the problem in the selected language.

Next, the student must go through a sequence of steps to have the problem correctly modeled as:

• Assigning variables: At the beginnig the student must choose variables to designate unknowns that are relevant to the problem. This includes the target unknowns (they appear as arguments of find clauses) and expressions like some apples.

• Discovering relations: In this step the student has to combine information from different statements into new relations. For example, decomposing the fruits that John has into the apples and bananas that John has.

• Stating equations: In the next step, the student converts the relations uncovered in the previous step into numerical equations. The system checks that they are consistent and are entailed by the problem information.

• Final: At the last step, the system displays the solution for the unknowns of the problem and exits.

• Saludes J, Caprotti O, Xambó S. A grammar-based approach to multilingual mathematics. 5th International Workshop on Mathematical e-Learning

• Archambault D, Caprotti O, Ranta A, Saludes J. Using GF in multimodal assistants for mathematics.

• Saludes J, Xambó S. Multilingual Sage. Tbilisi Mathematical Journal. 5(2) (in press)

• Saludes J, Xambó S. The GF Mathematics Library. Proceedings First Workshop on CTP Components for Educational Software (THedu'11). Electronic Proceedings in Theoretical Computer Science :102–110.

• Saludes J, Xambó S. Toward multilingual mechanized mathematics assistants. EACA 2012 (Proceedings).

• Ranta A. Translating between Language and Logic: What Is Easy and What is Difficult? CADE-23. Automated Deduction. LNCS/LNAI 6803:5-25