Constructive Geometric Constraint Solving as a General Framework for KR-Based Declarative Spatial Reasoning

Carl P. L. Schultz, Mehul Bhatt

Abstract: We present a robust and scalable KR-centered foundation for modularly supporting general declarative spatial representation and reasoning within diverse declarative programming AI frameworks. Based on Constructive Geometric Constraint Solving, our approach provides the foundations for mixed qualitative-quantitative reasoning about space - mereotopology, relative orientation, size, proximity - encompassing key application-driven capabilities such as qualification, spatial consistency solving, quantification, and dynamic geometry. The paper also demonstrates: (a) the framework with benchmark problems (e.g., contact and orientation problems) and applications in spatial Q/A; (b) integration with constraint logic programming, and (c) empirical results illustrating how the proposed encodings outperform existing methods by orders of magnitude on the selected problems.