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

TL;DR

This paper introduces 3D-nCDC-ASP, a novel ASP-based framework for reasoning about cardinal directions between extended 3D objects, extending CDC with default constraints for flexible spatial reasoning.

Contribution

It extends Cardinal Directional Calculus to 3D with default constraints and provides a formal ASP-based reasoning framework for spatial relations.

Findings

Proves soundness of 3D-nCDC-ASP.

Demonstrates applications in 3D spatial reasoning.

Enables consistency checking and explanation of constraints.

Abstract

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.