A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set Programming

• Published in: Theory and practice of logic programming 2018-07, Vol.18 (3-4), p.355-371
• Main Authors: BARYANNIS, GEORGE, TACHMAZIDIS, ILIAS, BATSAKIS, SOTIRIS, ANTONIOU, GRIGORIS, ALVIANO, MARIO, SELLIS, TIMOS, TSAI, PEI-WEI
• Format: Article
• Language: English
• Subjects: Calculus; Cognition & reasoning; Mathematical programming; Natural language (computers); Original Article; Qualitative reasoning; Reasoning; Spatial data; Trajectories
• ISSN: 1471-0684; 1475-3081
• DOI: 10.1017/S147106841800011X

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.