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Points in point-free mereotopology

Schoop D.J.

Fundamenta Informaticae

2001

Vol. 46, nr 1,2

129-143

It is considered the virtue of mereotopology that it takes regions instead of points to be the primitive entities of space. As mereotopology is assumed to avoid the difficulties incurred by considering points as primitive entities, mereotopology is thought to provide the means for common-sense spatial representation and reasoning. However, we show that considering regions as primitive entities in mereotopology does not prevent us referring to points in a commonly used mereotopological first-order language. Therefore, the difficulties attributed to taking points as primitive entities must be considered even for point-free mereotopologies. Consequently, the virtue of mereotopology cannot lie in taking regions instead of points as primitive entities. On the contrary, we argue that the virtue of mereotopology is its capability to treat regions and points as primitive entities.