Reasoning with Topological and Directional Spatial Information

TL;DR

This paper explores reasoning with combined topological and directional spatial information, demonstrating conditions under which the joint satisfaction problem can be efficiently separated and solved independently.

Contribution

It introduces a method to decompose combined topological and directional constraints into independent problems under certain subclasses, enabling polynomial-time solutions.

Findings

BIPATH algorithm is incomplete for basic RCC8 and RA constraints.

Separation of topological and directional constraints is possible within specific subclasses.

A method for approximate solutions to general RA constraints is proposed.

Abstract

Current research on qualitative spatial representation and reasoning mainly focuses on one single aspect of space. In real world applications, however, multiple spatial aspects are often involved simultaneously. This paper investigates problems arising in reasoning with combined topological and directional information. We use the RCC8 algebra and the Rectangle Algebra (RA) for expressing topological and directional information respectively. We give examples to show that the bipath-consistency algorithm BIPATH is incomplete for solving even basic RCC8 and RA constraints. If topological constraints are taken from some maximal tractable subclasses of RCC8, and directional constraints are taken from a subalgebra, termed DIR49, of RA, then we show that BIPATH is able to separate topological constraints from directional ones. This means, given a set of hybrid topological and directional constraints from the above subclasses of RCC8 and RA, we can transfer the joint satisfaction problem in polynomial time to two independent satisfaction problems in RCC8 and RA. For general RA constraints, we give a method to compute solutions that satisfy all topological constraints and approximately satisfy each RA constraint to any prescribed precision.