Proving completeness of OpenGIS SQL spatial relationships and operations

OpenGIS SQL is a standard for incorporating GIS and spatial concepts into SQL. Two types of methods are part of OpenGIS SQL: (1) boolean methods for topological relationships among spatial objects, and (2) methods for specifying spatial operations. We prove that the complete set of 2-dimensional spatial relationships defined by Egenhofer can all be specified using OpenGIS SQL operations and relationships. Our proof shows how each spatial relationship can be specified using OpenGIS SQL and thus provides users with the means of determining how each spatial relationship can be written in SQL. This provides users with enhanced usability and flexibility by providing the specific OpenGIS conditions for every possible 2-dimensional spatial relationship.