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An Incremental SAT-Based Approach to Reason Efficiently on Qualitative Constraint Networks

  • Gael GlorianEmail author
  • Jean-Marie Lagniez
  • Valentin Montmirail
  • Michael Sioutis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)

Abstract

The \({\mathcal {RCC}}8 \) language is a widely-studied formalism for describing topological arrangements of spatial regions. Two fundamental reasoning problems that are associated with \({\mathcal {RCC}}8 \) are the problems of satisfiability and realization. Given a qualitative constraint network (QCN) of \({\mathcal {RCC}}8 \), the satisfiability problem is deciding whether it is possible to assign regions to the spatial variables of the QCN in such a way that all of its constraints are satisfied (solution). The realization problem is producing an actual spatial model that can serve as a solution. Researchers in \({\mathcal {RCC}}8 \) focus either on symbolically checking the satisfiability of a QCN or on presenting a method to realize (valuate) a satisfiable QCN. To the best of our knowledge, a combination of those two lines of research has not been considered in the literature in a unified and homogeneous approach, as the first line deals with native constraint-based methods, and the second one with rich mathematical structures that are difficult to implement. In this article, we combine the two aforementioned lines of research and explore the opportunities that surface by interrelating the corresponding reasoning problems, viz., the problems of satisfiability and realization. We restrict ourselves to QCNs that, when satisfiable, are realizable with rectangles. In particular, we propose an incremental \(\mathrm {SAT}\)-based approach for providing a framework that reasons about the \({\mathcal {RCC}}8 \) language in a counterexample-guided manner. The incrementality of our approach also avoids the usual blow-up and the lack of scalability in \(\mathrm {SAT}\)-based encodings. Specifically, our \(\mathrm {SAT}\)-translation is parsimonious, i.e, constraints are added incrementally in a manner that guides the embedded \(\mathrm {SAT}\)-solver and forbids it to find the same counter-example twice. We experimentally evaluated our approach and studied its scalability against state-of-the-art solvers for reasoning about \({\mathcal {RCC}}8 \) relations using a varied dataset of instances. The approach scales up and is competitive with the state of the art for the considered benchmarks.

Keywords

\({\mathcal {RCC}} \) Qualitative Spatial and Temporal Reasoning \(\mathrm {SAT}\) \({\text {CEGAR}}\) 

Notes

Acknowledgments

The authors would like to thank the anonymous reviewers for their insightful comments. Part of this work was supported by the French Ministry for Higher Education and Research, the Haut-de-France Regional Council through the “Contrat de Plan État Région (CPER) DATA” and an EC FEDER grant.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Gael Glorian
    • 1
    Email author
  • Jean-Marie Lagniez
    • 1
  • Valentin Montmirail
    • 1
  • Michael Sioutis
    • 2
  1. 1.CRIL, Artois University and CNRSLensFrance
  2. 2.Örebro Universitet, MPI@AASSÖrebroSweden

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