Spatial relations between indeterminate regions Original Research Article

Systems of relations between regions are an important aspect of formal theories of spatial data. Examples of such relations are part-of, partially overlapping, and disjoint. One particular family of systems is that based on the region-connection calculus (RCC). These systems of relations were originally formulated for ideal regions, not subject to imperfections such as vagueness or indeterminacy. This paper presents two new methods for extending the relations based on the RCC from crisp regions to indeterminate regions. As a formal context for these two methods we develop an algebraic approach to spatial indeterminacy using Łukasiewicz algebras. This algebraic approach provides a generalisation of the “egg-yolk” model of indeterminate regions. The two extension methods which we develop are proved to be equivalent. In particular, it is shown that it is possible to define part-of in terms of connection in the indeterminate case. This generalises a well-known result about crisp RCC regions. Our methods of extension take a relation on crisp regions taking values in the set of two Boolean truth values, and produce a relation on indeterminate regions taking one of three truth values. We discuss how our work might be developed to give more detailed relations taking values in a six-element lattice.