Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.Comment: 10 pages, 4 figure

The Accessibility of Mathematical Notation on the Web and Beyond

This paper serves two purposes. First, it offers an overview of the role of the Mathematical Markup Language (MathML) in representing mathematical notation on the Web, and its significance for accessibility. To orient the discussion, hypotheses are advanced regarding users’ needs in connection with the accessibility of mathematical notation. Second, current developments in the evolution of MathML are reviewed, noting their consequences for accessibility, and commenting on prospects for future improvement in the concrete experiences of users of assistive technologies. Recommendations are advanced for further research and development activities, emphasizing the cognitive aspects of user interface design

Using Markup Languages for Accessible Scientific, Technical, and Scholarly Document Creation

In using software to write a scientific, technical, or other scholarly document, authors have essentially two options. They can either write it in a ‘what you see is what you get’ (WYSIWYG) editor such as a word processor, or write it in a text editor using a markup language such as HTML, LaTeX, Markdown, or AsciiDoc. This paper gives an overview of the latter approach, focusing on both the non-visual accessibility of the writing process, and that of the documents produced. Currently popular markup languages and established tools associated with them are introduced. Support for mathematical notation is considered. In addition, domain-specific programming languages for constructing various types of diagrams can be well integrated into the document production process. These languages offer interesting potential to facilitate the non-visual creation of graphical content, while raising insufficiently explored research questions. The flexibility with which documents written in current markup languages can be converted to different output formats is emphasized. These formats include HTML, EPUB, and PDF, as well as file formats used by contemporary word processors. Such conversion facilities can serve as means of enhancing the accessibility of a document both for the author (during the editing and proofreading process) and for those among the document’s recipients who use assistive technologies, such as screen readers and screen magnifiers. Current developments associated with markup languages and the accessibility of scientific or technical documents are described. The paper concludes with general commentary, together with a summary of opportunities for further research and software development