Querying Geometric Figures Using a Controlled Language, Ontological Graphs and Dependency Lattices
This work addresses the need for efficient query mechanisms in geometry education and automated theorem proving, though it appears incremental as it builds on existing approaches.
The paper tackles the problem of querying large repositories of geometric constructions by developing algorithms for querying both declarative and procedural descriptions of geometric figures, using dynamic geometry systems or a controlled natural language.
Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future enhanced educational software as well as in a next generation of mechanized mathematics assistants. Recently emerged Web repositories of geometric knowledge, like TGTP and Intergeo, are an attempt to make the already vast data set of geometric knowledge widely available. Considering the large amount of geometric information already available, we face the need of a query mechanism for descriptions of geometric constructions. In this paper we discuss two approaches for describing geometric figures (declarative and procedural), and present algorithms for querying geometric figures in declaratively and procedurally described corpora, by using a DGS or a dedicated controlled natural language for queries.