ASPMT(QS): Non-Monotonic Spatial Reasoning with Answer Set Programming Modulo Theories

TL;DR

ASPMT(QS) is a novel system for non-monotonic spatial reasoning that combines qualitative and geometric spatial information, effectively addressing indirect effects and ramification problems using SMT solvers.

Contribution

It introduces ASPMT(QS), a fully-implemented approach that integrates answer set programming with theories of real nonlinear arithmetic for dynamic spatial reasoning.

Findings

ASPMT(QS) uniquely handles indirect spatial effects.

It effectively combines qualitative and geometric spatial data.

The system outperforms other spatial reasoning tools in key tasks.

Abstract

The systematic modelling of \emph{dynamic spatial systems} [9] is a key requirement in a wide range of application areas such as comonsense cognitive robotics, computer-aided architecture design, 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 Sat 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 using choice formulas. 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 prominent contemporary spatial reasoning systems. Our results show that ASPMT(QS) is 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.