From Resolving Inconsistencies in Qualitative Constraints Networks to Identifying Robust Solutions: A Universal Encoding in ASP

Qualitative Constraint Networks (QCNs) are foundational to Qualitative Spatial and Temporal Reasoning (QSTR) for modelling real-world entity relations, facilitating decision-making and planning. However, perturbations or even inconsistencies in inputs may arise in various application contexts, such as from unforeseen circumstances or by merging data from different sources. Therefore, it is crucial for qualitative reasoning systems to address these challenges, e.g., not just identify any solution, but to optimize solutions for resilience against perturbations. Likewise, the ability is needed to resolve any inconsistencies with minimal repairs. Both tasks are challenging optimization problems on their own, as determining network consistency is already \(\textsf{NP}\) -hard for most qualitative constraint languages. In this paper, we present a universal encoding in Answer-Set Programming (ASP) to address these challenges. Our encoding allows for efficient resolution of both the robustness and repair problem by exploiting ASP optimization techniques. We demonstrate the effectiveness of our encoding in an experimental evaluation. Our results show that our encoding can match the state-of-the-art on some qualitative calculi in terms of computational efficiency. On top, our encoding offers a flexible and powerful framework for tackling optimization problems in qualitative reasoning systems.