# Non-Monotonic Spatial Reasoning with Answer Set Programming Modulo Theories

arXiv: https://arxiv.org/abs/1606.07860 · HTML: https://mlsanity.com/paper/1606.07860/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2016.

## Built on by (most cited first, 6 of 6)

- [First-Order Stable Model Semantics with Intensional Functions](https://mlsanity.com/paper/2307.10225/) (2023)
- [Movement Analytics: Current Status, Application to Manufacturing, and Future Prospects from an AI Perspective](https://mlsanity.com/paper/2210.01344/) (2022)
- [Neuro-Symbolic Spatio-Temporal Reasoning](https://mlsanity.com/paper/2211.15566/) (2022)
- [Towards a Neurosymbolic Reasoning System Grounded in Schematic Representations](https://mlsanity.com/paper/2509.03644/) (2025)
- [Answer Set Programming Energised! End-to-End Neurosymbolic Reasoning and Learning with ASP and Energy Based Models](https://mlsanity.com/paper/2607.08136/) (2026)
- [Logic, Optimization, and Artificial Intelligence](https://mlsanity.com/paper/2607.15532/) (2026)

## Abstract (arXiv)

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.