Interfaces for mathematical communication

Saturday, December 9, 2006 - 11:30am - 12:00pm
EE/CS 3-180
Elena Smirnova (University of Western Ontario), Stephen Watt (University of Western Ontario)
In this talk we discuss one of the essential aspects of mathematical communication: providing interfaces to mathematical environments. This involves mathematical data and knowledge representation, communication protocols and organization of digital libraries. Each of these three subjects represents a complex problem studied extensively for the past decades. We present an overview of the state-of-the-art that has been developed over the course of several research networks connecting two large communities: mathematical knowledge management and mathematical communication. In this talk we report on the main outcomes of these projects that have been achieved both in collaboration and independently by our group at the Ontario Research Centre for Computer Algebra.

First, we briefly address the issues accompanying the problem of mathematical knowledge representation, such as customizing notation for mathematical content and translation between most popular mathematical data formats. We describe how these problems can be approached to ensure conservation of high-level semantic content.

Secondly, we describe an approach to providing interoperability between different mathematical environments. We concentrate on system-independent standards, designed to describe mathematical content and problem domains. These comprise languages and ontologies developed by the MONET (Mathematics On the NET) Consortium to enable unambiguous communication between distributed mathematical components.

Finally, we discuss the problem of creation and organization of databases to store mathematical context. We present our approach to collecting and storing the information about mathematical content, retrieved from web-based mathematical archives. We demonstrate the use of these databases by the example of assisting in on-line mathematical handwriting analysis. Specifically, we show how we use the information derived from the analysis of a digital libraries to prioritize character choices in a mathematical handwriting application.