From the Egg-Yolk to the Scrambled-Egg Theory

The way we deal with space in many everyday situations is on a qualitative basis, allowing for imprecision in spatial descriptions when we interact with each other. This is often achieved by specifying the spatial relations between the objects or regions that we talk about. In artificial intelligence, a variety of formalisms have been developed that deal with space on the basis of relations between objects or regions that objects might occupy. One of these formalisms is the RCC theory, which is based on a primitive relation, called connectedness, and uses a set of topological relations, defined on the basis of connectedness, to provide a framework to reason about regions. This paper discusses an extension of the RCC theory, which deals with vagueness in spatial representations. The extension is based on the egg-yolk theory, but unlike the egg-yolk theory uses fuzzy logic to express vagueness.