A Dynamical Document Structure to Capture the Semantics of Mathematical Concepts

A grammar-based approach to the specification of mathematical notation is proposed. The method is based on a meta-structure using attributed context-free grammars for capturing the meaning of mathematical concepts. The proposal is based on an authoring model which addresses the user needs as a fundamental requirement. It is structured around a scope mechanism allowing the mapping between semantics and syntax to be modified at any time during authoring. This process supports the dynamics of the meaning-to-syntax binding necessary in the authoring of mathematical concepts. Modular grammar fragments characterized by a one-to-one mapping between mathematical concept and grammar representation provide the adequate support for the definition of the various scopes. An incremental update process is defined to modify the grammar fragments which support the changes needed in the authoring process.