Link between the whole et its parts in UML representations of spatial aggregations: an application in the context of geographic databases

Extended relational models used for geographic databases allow to store spatial data. Indeed, the common extension consists in adding a special attribute in tables; the values of this attribute in database instances are collections of geometries. Computer scientifists need to exactly know what types of geometries they will find in tables resulting from aggregation, particulary when they will write program code that queries the database. Indeed, they have to precisely identify what are the types of geometries (point, polyline,~)extracted by computer-based applications from whole instances. Thus, the main purpose works presented in this paper consists in defining solutions to deduce the geometry types stored in a whole from the geometry types of its parts. This computation is made from UML specifications of spatial aggregation operations in considering that geometry types of input tables are known.The objective is to propose a mechanism to determine spatial types allowed in the attribute geometry values of Country and Continent whole instances. In fact, our works respond to the question "what can contain values of the geometry attribute in a whole table? one point? several points? several points and several polygons? several points or several polygons? the same number of points as the number of polygons? ...".