An Exploratory Survey of Logic-Based Formalisms for Spatial Information

This chapter presents a tentative survey of logic-based formalisms for representing various aspects of spatial information ranging from the expression of spatial relationships between regions to the attribution of properties to definite regions. The first main part of the paper reviews the logic-based representations of mereotopologies in classical or modal logics, and in fuzzy and rough sets settings, as well as modal logic representations of geometries. The second main part is devoted to the handling of properties associated to regions. The association either relates properties to a current region of interest, or to explicitly named regions. Properties may be attached to a whole region and hold “everywhere”, or hold “somewhere”, or “elsewhere”. Properties and their localization may be also pervaded with uncertainty. This overview reveals that the many existing formalisms address different issues, and when they deal with the same issue they do it differently. However, it seems that in practice there is a need for a combination of representational capabilities, which could cover both spatial relationships and localized properties, possibly in presence of uncertainty.