Spatial Symmetry Driven Pruning Strategies for Efficient Declarative Spatial Reasoning

TL;DR

This paper introduces a novel symmetry-based pruning algorithm for declarative spatial reasoning that significantly enhances computational efficiency, enabling practical solutions to complex geometric and qualitative spatial problems.

Contribution

The paper presents a new symmetry-driven pruning strategy integrated into CLP(QS) that drastically improves spatial reasoning performance over traditional polynomial constraint methods.

Findings

Outperforms conventional polynomial encodings by orders of magnitude

Enables solving previously intractable spatial reasoning problems

Effective across contact, mereology, and geometry benchmarks

Abstract

Declarative spatial reasoning denotes the ability to (declaratively) specify and solve real-world problems related to geometric and qualitative spatial representation and reasoning within standard knowledge representation and reasoning (KR) based methods (e.g., logic programming and derivatives). One approach for encoding the semantics of spatial relations within a declarative programming framework is by systems of polynomial constraints. However, solving such constraints is computationally intractable in general (i.e. the theory of real-closed fields). We present a new algorithm, implemented within the declarative spatial reasoning system CLP(QS), that drastically improves the performance of deciding the consistency of spatial constraint graphs over conventional polynomial encodings. We develop pruning strategies founded on spatial symmetries that form equivalence classes (based on affine transformations) at the qualitative spatial level. Moreover, pruning strategies are themselves formalised as knowledge about the properties of space and spatial symmetries. We evaluate our algorithm using a range of benchmarks in the class of contact problems, and proofs in mereology and geometry. The empirical results show that CLP(QS) with knowledge-based spatial pruning outperforms conventional polynomial encodings by orders of magnitude, and can thus be applied to problems that are otherwise unsolvable in practice.