A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set Programming

TL;DR

This paper introduces two new trajectory calculi for qualitative spatial reasoning, implemented in Answer Set Programming, and demonstrates their scalability and effectiveness on real-world data for trajectory consistency problems.

Contribution

It proposes two novel trajectory calculi based on allowed properties, with multiple ASP encodings, and provides experimental evaluation showing improved scalability over previous methods.

Findings

Best implementation scales up to 250 trajectories for TC-6

Achieves 150 trajectories for TC-10 in consistency problems

Significantly outperforms previous ASP approaches

Abstract

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their paths. In this work, we propose two versions of a trajectory calculus based on the allowed properties over trajectories, where trajectories are defined as a sequence of non-overlapping regions of a partitioned map. More specifically, if a given trajectory is allowed to start and finish at the same region, 6 base relations are defined (TC-6). If a given trajectory should have different start and finish regions but cycles are allowed within, 10 base relations are defined (TC-10). Both versions of the calculus are implemented as ASP programs; we propose several different encodings, including a generalised program capable of encoding any qualitative calculus in ASP. All proposed encodings are experimentally evaluated using a real-world dataset. Experiment results show that the best performing implementation can scale up to an input of 250 trajectories for TC-6 and 150 trajectories for TC-10 for the problem of discovering a consistent configuration, a significant improvement compared to previous ASP implementations for similar qualitative spatial and temporal calculi. This manuscript is under consideration for acceptance in TPLP.