Order in space: a general formalism for spatial reasoning

We propose a general approach for reasoning in space. The approach is composed of a set of two general constraints to govern the spatial relationships between objects in space, and two rules to propagate relationships between those objects. The approach is based on a uniform representation of the topology of the space as a connected set of components using a structure called adjacency matrix which can capture the topology of objects of different complexity in any space dimension. The relationships between objects are represented by the intersection of the space components. The approach is also shown to be applicable to reasoning in the temporal domain and is used to explain the conceptual neighbourhood phenomenon related to the reasoning process. A major advantage of the method is that reasoning between objects of any complexity can be achieved in a defined limited number of steps. Hence, the incorporation of spatial reasoning mechanisms in spatial information systems becomes possible.