Expressivity in polygonal, plane mereotopology

In recent years, there has been renewed interest in the development of form al languages for describing mereological (part-whole) and topological relat ionships between objects in space. Typically, the non-logical primitives of these languages are properties and relations such as 'x is connected' or ' x is a part of y', and the entities over which their variables range are, a ccordingly, not points, but regions: spatial entities other than regions ar e admitted, if at all, only as logical constructs of regions. This paper co nsiders two first-order mereotopological languages, and investigates their expressive power. It turns out that these languages, notwithstanding the si mplicity of their primitives, are surprisingly expressive. In particular, i t is shown that infinitary versions of these languages are adequate to expr ess (in a sense mode precise below) all topological relations over the doma in of polygons in the closed plane.