Semester 3, Jacobs

Enviado por Mueller, Christine el Mié, 2007/10/24 - 09:54.

Reporting_period:

Semester 3: 1/08/07 - 31/01/08

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mmlkit - a toolkit for presenting content MathML and OpenMath

mmlkit is a Java-based toolkit for building presentation engines for content markup formats for mathematics.

The next generation of content markup formats for mathematics come with a flexible mechanism for defining mathematical notations (see e.g. the MathML3 Working Draft. mmlkit facilitates building presentation engines that use such notation definitions as a parameter. For further information please refer to the project website.

SWiM

SWiM is a semantic wiki for mathematical knowledge management. Its documents are encoded in OMDoc and displayed in XHTML+MathML, and an RDF-based semantic web infrastructure is used to exploit knowledge extracted from the documents in order to offer services to the users.

The Core System

Recent steps in the development of SWiM have been the upgrade of the whole system to IkeWiki 2.0alpha, which offers a completely redesigned AJAX-powered user interface that offers more possibilities for interaction and reacts faster to user input. In the wiki editor, text sections can be annotated to represent items of mathematical knowledge (e. g. proofs), OpenMath formulae can be entered in a simple ASCII syntax, and natural-language sections can be visually edited like HTML. For the rendering of mathematical formulae from content markup to presentation markup, notation definitions in the new MathML 3 content dictionary sublanguage are used; the actual rendering is carried out by the MML-Proc renderer. Moreover, a basic import and export of OMDoc documents to and from the wiki is now working.

The next planned steps are allowing notation definitions to be distributed over multiple pages (representing different content dictionaries) in the wiki, which will allow for visually debugging content dictionaries in SWiM. The import/export feature will be enhanced to allow for wiki pages conveniently being edited in locally installed (math) editors. Further envisaged steps, including semantic editing services based on an OMDoc document ontology, are listed on the SWiM development roadmap.

The Flyspeck Wiki Case Study

In order to gain an intuition about what other services mathematicians may need in a wiki, we are working on a case study in supporting the Flyspeck project with a semantic wiki. The objective of Flyspeck is to work out a formal and computer-veri?able proof of the Kepler conjecture about sphere packing. We believe that using a semantic wiki can support certain work?ows in this ambitious project – for example keeping track of which sub-theorems have already been proven formally, and giving the community the possibility to get involved. While the long-term goal is to offer this support in SWiM, using OMDoc as the exchange format between the languages of various automated theorem provers, and offering editing services specially tailored to mathematical documents, we are currently conducting a pre-study in an enhanced Semantic MediaWiki, whose results will then contribute to the further development of SWiM.

ArXMLiv

The last few years have seen the emergence of various content-oriented XML-based, content-oriented markup languages for mathematics and natural sciences on the web, e.g. OpenMath, Content MathML, or our own OMDoc and PhysML. These representation languages mathematics, that makes the structure of the mathematical knowledge in a document explicit enough that machines can operate on it. The promise if these content-oriented approaches is that various tasks involved in ``doing mathematics'' (e.g. search, navigation, cross-referencing, quality control, user-adaptive presentation, proving, simulation) can be machine-supported, and thus the working mathematician is relieved to do what humans can still do infinitely better than machines.

In the arXMLiv project we try to translate the vast collection of scientific knowledge captured in the arXiv repository into content-based form, so that we can use it as a basis for added-value services.

We are using Bruce Miller's LaTeXML system for transforming LaTeX documents to XHTML with Presentation MathML. LaTeXML is a reimplementation of the TeX parser with a programmable XML emitter. The main advantage of the system is that we can control macro expansion by supplying customized "LaTeXML bindings" for the macros. These are instructions to the emitter to directly construct output XML instead of expanding the macro to TeX primitives.

The main technical task of the arXMLiv project is to supply LaTeXML bindings for the (thousands of) LaTeX classes and packages used in the arXiv collections. For this we have developed a distributed build system that continuously runs LaTeXML over the arXiv collection and collects statistics about e.g. the most sorely missing LaTeXML bindings.

We have processes more than half of the arXiv collection (one run is a processor-year-size undertaking) and already have a success rate of over 50% (i.e. over 50% of the documents ran through without LaTeXML noticing an error).

OMBase

OMBase is a database for mathematical documents that in its first prototype implements HTTP operations through a REST (Representational State Transfer) interface. It is designed to support files stored in OMDoc format. We see OMBase to be a component integrated into other frameworks, as a reliable and transparent storing tool for other e.g. educational content.

panta rhei

During the summer, the panta rhei system has been implemented which aims at promoting the learning experience of students by explicating teachers' and students' characteristics and practices (available at http://kwarc.info/projects/panta-rhei/demo/htdocs/; you can log in with username ``defaultUser and password ``init01) from their documents e.g. slides, homework, and forum postings. Currently, the system enables the rating and annotation of semantically marked up documents and their fragments (e.g. definitions, examples, theories) via a forum-like infrastructure (see the result of the first JEM case study.

Based on all users' documents, the system can explicate the relevance of document fragments or ``object of interest'' in the respective lecture. This is one step towards explicating the users' practice in terms of their interest. The first mock-up of panta rhei will suit for a more sophisticated and document-based analysis of practice.

Currently, the system is extended towards the explanation of notations in the lecture notes in comparison to the notations the students have become used to during their high school education. For this, the group is currently analyzing the various notations in a fundamental lecture on General Computer Science. Moreover, students are interviewed (since they have been educated in various countries and might therefore been trained to use very different notations than those of the lecturer). Moreover, KWARC is currently contributing to the revised MathML specification (http://www.w3.org/Math/) towards a more sophisticated representation of mathematical concepts in scientific documents. We are also implementing the generation of different renderings/ notations for these concepts. The result will be integrated into panta rhei, allowing the system to extract mathematical concepts as well as provide alternative renderings/ notations for the same concept.