Abstract

We present a formal framework and implementation for declarative spatial representation and reasoning about the topological relationships between boolean combinations of regions (i.e., union, intersection, difference, xor). Regions of space here correspond to arbitrary axis aligned n-polytope objects, with geometric parameters either fully grounded, partially grounded, or completely unspecified. The framework is implemented in the context of CLP([Qscr ][Sscr ])

CLP([Qscr ][Sscr ]): A Declarative Spatial Reasoning System. www.spatial-reasoning.com

, a constraint logic programming based declarative spatial reasoning system providing support for geometric and qualitative spatial abstraction and inference capabilities.

We demonstrate that our method can solve packing, contact, containment, and constructive proof problems that are unsolvable using standard relational algebraic approaches for qualitative spatial reasoning (QSR). Our approach is driven by general accessibility of spatial reasoning via KR languages for their application in domains such as design, geography, robotics, and cognitive vision.