A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set Programming

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.

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

“…whether the set is consistent). This problem is formalised in the next definition, following the equivalent definition by Baryannis et al (2018). Note that in Definition 3.2 the composition and converse operations are of the weak variant as defined by Dylla et al (2017), since all existing binary calculi define at least weak operations.…”

“…ASP allows for solving hard search and optimisation problems, and reasoning with qualitative relations is one such problem. Previous research (Li 2012;Brenton et al 2016; Baryannis et al 2018) has shown that ASP is capable of expressing different qualitative calculi and several different encodings have been proposed with varying levels of performance and applicability. Also, the logic programming nature of ASP means that encodings are human-readable and configurable which is in line with the notion of prioritising comprehensibility that underlies qualitative reasoning.…”

“…Subsequent work by Brenton et al (2016) and Baryannis et al (2018) proposed a number of ASP encodings of qualitative calculi that improve on the ones by Li, while Izmirlioglu and Erdem (2018) also proposed such encodings but only for the particular case of the cardinal direction calculus. The present work builds on the generalised ASP encoding developed by Baryannis et al (2018), proposing a family of encodings grounded in a formalisation of qualitative calculi similarly to Dylla et al (2017). These econdings can be used to represent any binary quantitative calculus and perform reasoning including both qualitative and non-qualitative aspects as required for the motivating case study.…”

Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming

“…For instance, Brenton et al (2016) represent Region Connection Calculus with eight base relations (RCC-8) (Cohn et al 1997), Walega et al (2017) represent RCC-5 (David A. Randell and Cohn 1992), and Baryannis et al (2018) represent Trajectory Calculus (Baryannis et al 2018) in ASP. Like (Brenton et al 2016) and (Baryannis et al 2018), we utilize the ASP language ASP-Core-2 and the ASP solver CLINGO ; (Walega et al 2017) utilizes ASPMT language, and the SMT solver Z3 (de Moura and Bjørner 2008).…”

“…Randell and Cohn 1992), and Baryannis et al (2018) represent Trajectory Calculus (Baryannis et al 2018) in ASP. Like (Brenton et al 2016) and (Baryannis et al 2018), we utilize the ASP language ASP-Core-2 and the ASP solver CLINGO ; (Walega et al 2017) utilizes ASPMT language, and the SMT solver Z3 (de Moura and Bjørner 2008). Different from these studies: (a) we consider a 3D qualitative calculus, and extend it with new types of default constraints whose semantics is provided by means of the nonmonotonic constructs of ASP.…”