Topological Relations Based on Part and Complement

Classiications of the relationship between two spatial regions have been widely studied and include the 4-intersection and 9-intersection models of Egenhofer, and the RCC5 and RCC8 schemes of Cohn and his colleagues. This paper presents a new way of describing the RCC5 relation between two regions. The technique depends only on the notions of part and complement, and the central theme of the paper is that the appropriate way to develop analogues of RCC5 (and related systems) in contexts other than crisp regions is simply to use the appropriate notions of part and complement in the new context. The approach to RCC5 in this paper allows the empty region without introducing any diiculties. The use of the technique to deal with RCC8, and also to clarify the relationship of RCC8 to the 9-intersection model, is discussed. The paper includes a new generic approach to vague regions, based on the semantics of a vague region being a set of crisp regions. It is shown that one notion of part for this type of vague region takes values in a lattice of six truth values. These truth values have straightforward interpretations in terms of possible crispings of vague regions. This notion of part leads to a scheme for classifying relationships between vague regions. The paper also explains how the techniques developed can be applied to spatial regions which vary over time.