Region-based Qualitative Geometry

We present a highly expressive logical language for describing qualitative con gurations of spatial regions. We call the theory Region Based Geometry (RBG). Our axiomatisation is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. We show that our theory is categorical: all models are isomorphic to a classical interpretation in terms of Cartesian spaces over R. We investigate the 2nd-order character ofRBG and prove incompleteness of some weaker 1st-order variants. We show that within this theory the concept of sphere and the congruence relation are interde nable. We indicate how our theory might be applied to practical problems in knowledge representation by de ning concepts that can be used for representing and reasoning about the motion of rigid bodies within a con ning environment.