Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming
This work addresses the problem of spatial reasoning in 3D environments for domains like robotics or GIS, but it is incremental as it extends prior 2D and default constraint methods to 3D.
The paper tackles the problem of representing and reasoning about cardinal directions between extended objects in 3D space by proposing a novel formal framework called 3D-nCDC-ASP, which extends existing calculi and provides capabilities for nonmonotonic reasoning, consistency checking, inconsistency explanation, and inference of missing relations, with soundness proven and applications illustrated.
We propose a novel formal framework (called 3D-nCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-nCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and nCDC-ASP to 3D. 3D-nCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-nCDC-ASP, and illustrate its usefulness with applications. This paper is under consideration for acceptance in TPLP.