Prime Scenarios in Qualitative Spatial and Temporal Reasoning

Authors Yakoub Salhi , Michael Sioutis

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Author Details

Yakoub Salhi
  • CRIL UMR 8188, Université d'Artois & CNRS, France
Michael Sioutis
  • LIRMM UMR 5506, Université de Montpellier & CNRS, France

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Yakoub Salhi and Michael Sioutis. Prime Scenarios in Qualitative Spatial and Temporal Reasoning. In 30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The concept of prime implicant is a fundamental tool in Boolean algebra, which is used in Boolean circuit design and, recently, in explainable AI. This study investigates an analogous concept in qualitative spatial and temporal reasoning, called prime scenario. Specifically, we define a prime scenario of a qualitative constraint network (QCN) as a minimal set of decisions that can uniquely determine solutions of this QCN. We propose in this paper a collection of algorithms designed to address various problems related to prime scenarios. The first three algorithms aim to generate a prime scenario from a scenario of a QCN. The main idea consists in using path consistency to identify the constraints that can be ignored to generate a prime scenario. The next two algorithms focus on generating a set of prime scenarios that cover all the scenarios of the original QCN: The first algorithm examines every branch of the search tree, while the second is based on the use of a SAT encoding. Our last algorithm is concerned with computing a minimum-size prime scenario by using a MaxSAT encoding built from countermodels of the original QCN. We show that this algorithm is particularly useful for measuring the robustness of a QCN. Finally, a preliminary experimental evaluation is performed with instances of Allen’s Interval Algebra to assess the efficiency of our algorithms and, hence, also the difficulty of the newly introduced problems here.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Computing methodologies → Temporal reasoning
  • Computing methodologies → Spatial and physical reasoning
  • Spatial and Temporal Reasoning
  • Qualitative Constraints
  • Prime Scenario
  • Prime Implicant
  • Robustness Measurement


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