Multidimensional geospatial databases (also called « geospatial data cubes ») are the cornerstone of the emerging Spatial On-Line Analytical Processing technology (SOLAP). They are aimed at supporting Geographic Knowledge Discovery
(GKD) as well as certain types of spatial decision-making. Although these technologies seem promising at first glance, they may provide unreliable results if one does not consider the quality of spatio-temporal data. In traditional spatial databases, spatial integrity constraints have been employed to improve internal quality of spatial data. However, geospatial data cubes require additional integrity constraints in comparison to the traditional databases found into transactional GIS systems. These extra constraints concern the supplementary information included in these data cubes such as aggregated data, multidimensional cross-tabulation of data, and the existence of a temporal dimension with several levels of granularity. In this paper, we present the characteristics of geospatial data cubes that require innovative spatial integrity constraints. Then, we propose fundamental considerations for the classification of these integrity constraints and for the use of specification languages tailored for aggregative spatio-temporal integrity constraints. Finally, we address some questions that contribute to a research agenda for the definition of spatial integrity constraints in geospatial data cubes.