A Survey on Retrieval of Mathematical Knowledge

We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page

VMEXT: A Visualization Tool for Mathematical Expression Trees

Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Typically, researchers and practitioners manually visualize expression trees using general-purpose tools. This approach is laborious, redundant, and error-prone. Manual visualizations represent a user's notion of what the markup of an expression should be, but not necessarily what the actual markup is. This paper presents VMEXT - a free and open source tool to directly visualize expression trees from parallel MathML. VMEXT simultaneously visualizes the presentation elements and the semantic structure of mathematical expressions to enable users to quickly spot deficiencies in the Content MathML markup that does not affect the presentation of the expression. Identifying such discrepancies previously required reading the verbose and complex MathML markup. VMEXT also allows one to visualize similar and identical elements of two expressions. Visualizing expression similarity can support support developers in designing retrieval approaches and enable improved interaction concepts for users of mathematical information retrieval systems. We demonstrate VMEXT's visualizations in two web-based applications. The first application presents the visualizations alone. The second application shows a possible integration of the visualizations in systems for mathematical knowledge management and mathematical information retrieval. The application converts LaTeX input to parallel MathML, computes basic similarity measures for mathematical expressions, and visualizes the results using VMEXT.Comment: 15 pages, 4 figures, Intelligent Computer Mathematics - 10th International Conference CICM 2017, Edinburgh, UK, July 17-21, 2017, Proceeding

The MMT API: A Generic MKM System

The MMT language has been developed as a scalable representation and interchange language for formal mathematical knowledge. It permits natural representations of the syntax and semantics of virtually all declarative languages while making MMT-based MKM services easy to implement. It is foundationally unconstrained and can be instantiated with specific formal languages. The MMT API implements the MMT language along with multiple backends for persistent storage and frontends for machine and user access. Moreover, it implements a wide variety of MMT-based knowledge management services. The API and all services are generic and can be applied to any language represented in MMT. A plugin interface permits injecting syntactic and semantic idiosyncrasies of individual formal languages.Comment: Conferences on Intelligent Computer Mathematics (CICM) 2013 The final publication is available at http://link.springer.com

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

Technologies for teaching mathematics via the world wide web

Published ArticleThis paper tries to find answers to the question concerning the availability of suitable technologies to accommodate the teaching and learning of mathematics by means of the World Wide Web. It addresses three standards for the presentation of content mark-up and touches on the importance of adequate browser applicability with respect to MathML as one of the standards. Various tools for rendering MathML on the web, as well as plug-ins and extensions and other combinations of technologies, are discussed. The paper concludes with the introduction of a dynamic mathematics object model (DMOM) by Robert Miner from Design Science Inc. Requirements for a DMOM are formulated and its implementation is discussed

OntoMathPROOntoMath^{PRO} Ontology: A Linked Data Hub for Mathematics

In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.Comment: 15 pages, 6 images, 1 table, Knowledge Engineering and the Semantic Web - 5th International Conferenc