Algebraic Reasoning for Uncertain Data
Raisonnement algébrique pour des données incertaines
Résumé
This chapter describes the basic principles of spatial reasoning processes based on algebras, independently of the imperfect dimension of spatial data. After putting forward some definitions, it also describes temporal and spatial models funded on algebras, especially RCC8 (Region Connection Calculus) for topological relations. The chapter presents related works and mentions some implementations of these models. Lattices are models that can suitably represent the algebras used for temporal or spatial relations. Due to their hierarchical structure, they can appropriately represent bodies of knowledge and the associated reasoning processes. Moreover, under certain conditions, they can establish a link between geographic information and spatial knowledge. Awareness of the uncertainty and imprecision associated with geographic information has resulted in the creation of models of objects with broad boundaries. The chapter examines some sets of relations for fuzzy spatial objects on which algebraic reasoning can be used.