  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.
