A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set
  Programming
  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.
