Non-Monotonic Spatial Reasoning with Answer Set Programming Modulo Theories

TL;DR

This paper introduces ASPMT(QS), a novel system for non-monotonic spatial reasoning that integrates geometric and qualitative data using Answer Set Programming Modulo Theories, capable of handling indirect effects and dynamic spatial systems.

Contribution

The paper presents ASPMT(QS), the first system to combine non-monotonic reasoning with geometric and qualitative spatial data within an ASPMT framework, addressing the ramification problem.

Findings

ASPMT(QS) effectively reasons about indirect spatial effects.

It outperforms other systems in spatial reasoning tasks.

It successfully integrates geometric and qualitative spatial information.

Abstract

The systematic modelling of dynamic spatial systems is a key requirement in a wide range of application areas such as commonsense cognitive robotics, computer-aided architecture design, and dynamic geographic information systems. We present ASPMT(QS), a novel approach and fully-implemented prototype for non-monotonic spatial reasoning -a crucial requirement within dynamic spatial systems- based on Answer Set Programming Modulo Theories (ASPMT). ASPMT(QS) consists of a (qualitative) spatial representation module (QS) and a method for turning tight ASPMT instances into Satisfiability Modulo Theories (SMT) instances in order to compute stable models by means of SMT solvers. We formalise and implement concepts of default spatial reasoning and spatial frame axioms. Spatial reasoning is performed by encoding spatial relations as systems of polynomial constraints, and solving via SMT with the theory of real nonlinear arithmetic. We empirically evaluate ASPMT(QS) in comparison with other contemporary spatial reasoning systems both within and outside the context of logic programming. ASPMT(QS) is currently the only existing system that is capable of reasoning about indirect spatial effects (i.e., addressing the ramification problem), and integrating geometric and qualitative spatial information within a non-monotonic spatial reasoning context. This paper is under consideration for publication in TPLP.