A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set Programming
This work addresses practical applications like bus route planning by enabling reasoning over qualitative spatial terms for moving objects, representing an incremental improvement over existing ASP methods for similar calculi.
The authors tackled the problem of qualitative spatial reasoning for moving objects by proposing two trajectory calculi (TC-6 and TC-10) based on allowed properties over trajectories, implemented in Answer Set Programming (ASP). Experimental results showed that their best implementation scales to 250 trajectories for TC-6 and 150 trajectories for TC-10 for discovering consistent configurations, a significant improvement over previous ASP implementations.
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.