The space algebra: spatial reasoning without composition tables

We propose a general approach for reasoning with incomplete topological knowledge in space without the need for composition tables. The approach builds on and generalizes our earlier formalism where spatial relations are represented by the intersection of object and space components. The reasoning method is applicable to objects of arbitrary complexity. One general equation is proposed here for the propagation of intersections between object components and the derivation of the result of spatial composition. Hence, a general algebra for reasoning in space is proposed. A major advantage of this method is that reasoning with incomplete knowledge can be done by direct application of the equation and the algebra on any spatial objects considered, and this eliminates the need for utilizing the inordinate number of composition tables which must be built for specific object types and topology. The method is applied on spatial objects of arbitrary complexity and in a finite definite number of steps controlled by the complexity needed in the representation of objects and the granularity of the spatial relations required