Qualitative reasoning about cardinal directions between spatial objects using answer set programming

Official URL: https://risc01.sabanciuniv.edu/record=b2486478_(Table of contents)

Qualitative spatial reasoning studies representation and reasoning with different aspects of space, such as direction, distance, size using parts of natural language rather than quantitative data. Qualitative models are useful in contexts where quantitative data is not available due to incomplete knowledge or uncertainty. Qualitative reasoning is also relevant for contexts with complete information and quantitative data because human agents tend to express spatial relation or configuration by means of qualitative terms for the sake of sociable and convenient communication. We introduce a novel formal framework (called NCDC-ASP ) for qualitative reasoning about cardinal directions between spatial objects on a plane, based on Cardinal Directional Calculus (CDC) and using Answer Set Programming (ASP), and extend it further (called 3D-NCDC-ASP ) to 3-dimensional space. Each framework provides solutions to all consistency checking problems in CDC (i.e., for a complete/incomplete set of basic/disjunctive CDC constraints over connected/disconnected spatial objects); many of these consistency checking problems are NP-complete and cannot be solved with the existing systems. Furthermore, each framework extends CDC with novel types of constraints (i.e., default CDC constraints and inferred CDC constraints) to offer other types of reasoning as well (i.e., commonsense reasoning, nonmonotonic reasoning with defaults, explanation generation for inconsistencies, and inference of missing cardinal directional relations). We prove the soundness and completeness of both NCDC-ASP and 3D-NCDC-ASP , comprehensively evaluate their computational efficiency, and illustrate their usefulness with applications in different domains ranging from underwater robotics to digital forensics