Discrete Mereotopology

Abstract

Whereas mereology, in the strict sense, is concerned solely with the part–whole relation, mereotopology extends mereology by including also the notion of connection, enabling one to distinguish, for example, between internal and peripheral parts, and between contact and separation. Mereotopology has been developed particularly within the Qualitative Spatial Reasoning research community, where it has been applied to, amongst other areas, geographical information science and image analysis. Most research in mereotopology has assumed that the entities being studied may be subdivided without limit, but a number of researchers have investigated mereotopological structures based on discrete spaces in which entities are built up from atomic elements that are not themselves subdivisible. This chapter presents an introductory treatment of mereotopology and its discrete variant, and provides references for readers interested in pursuing this subject in further detail.