The best way to make cooperate heterogeneous GIS (Geographical Information Systems) is to integrate them through a federated architecture. This last one necessitates in its first step the definition of a Canonical Data Model (CDM). The GEOgraphical COOPerative Model (GEOCOOPM) we have defined belongs to the family of terminological systems also known as description logics. We develop, in this paper, a precise syntax and semantic of Geocoopm and demonstrate the following: (1) First, Geocoopm gives a semantic to the spatial dimension. (2) It also permits the definition of heterogeneous data types (maps, numerical data, spatial data). (3) Geocoopm can represent various transformations on these data. (4) Finally, it provides a great facility for a good organisation of data and transformations using the subsumption function which enables building many hierarchies of data and transformations. This is a first step towards the schema integration process. We provide many examples to illustrate our claims.