Granularity in relational formalisms - With application to time and space representation

Temporal and spatial phenomena can be seen at a more or less precise granul arity, depending on the kind of perceivable details. As a consequence, the relationship between two objects may differ depending on the granularity co nsidered. When merging representations of different granularity, this may r aise problems. This paper presents general rules of granularity conversion in relation algebras. Granularity is considered independently of the specif ic relation algebra, by investigating operators for converting a representa tion from one granularity to another and presenting six constraints that th ey must satisfy. The constraints are shown to be independent and consistent and general results about the existence of such operators are provided. Th e constraints are used to generate the unique pairs of operators for conver ting qualitative temporal relationships (upward and downward) from one gran ularity tu another. Then two fundamental constructors (product and weakenin g) are presented: they permit the generation of new qualitative systems (e. g. space algebra) from. existing ones. They are shown to preserve most of t he properties of granularity conversion operators.