Reasoning about Qualitative Direction and Distance between Extended Objects using Answer Set Programming

TL;DR

This thesis develops an answer set programming framework to model and reason about qualitative spatial relations, including direction and distance, between extended objects with extensions for defaults, preferences, and negation.

Contribution

It introduces nCDC and nCDC+ frameworks that extend existing qualitative spatial calculi with new constraints and reasoning capabilities using ASP.

Findings

Framework effectively checks consistency of spatial relations.

Enables inference of missing or unknown relations.

Supports configuration of objects satisfying spatial queries.

Abstract

In this thesis, we introduce a novel formal framework to represent and reason about qualitative direction and distance relations between extended objects using Answer Set Programming (ASP). We take Cardinal Directional Calculus (CDC) as a starting point and extend CDC with new sorts of constraints which involve defaults, preferences and negation. We call this extended version as nCDC. Then we further extend nCDC by augmenting qualitative distance relation and name this extension as nCDC+. For CDC, nCDC, nCDC+, we introduce an ASP-based general framework to solve consistency checking problems, address composition and inversion of qualitative spatial relations, infer unknown or missing relations between objects, and find a suitable configuration of objects which fulfills a given inquiry.