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Collective Singleton-Based Consistency for Qualitative Constraint Networks

Authors Michael Sioutis, Anastasia Paparrizou, Jean-François Condotta

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Michael Sioutis
Anastasia Paparrizou
Jean-François Condotta

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Michael Sioutis, Anastasia Paparrizou, and Jean-François Condotta. Collective Singleton-Based Consistency for Qualitative Constraint Networks. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 19:1-19:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


Partial singleton closure under weak composition, or partial singleton (weak) path-consistency for short, is essential for approximating satisfiability of qualitative constraints networks. Briefly put, partial singleton path-consistency ensures that each base relation of each of the constraints of a qualitative constraint network can define a singleton relation in the corresponding partial closure of that network under weak composition, or in its corresponding partially (weak) path-consistent subnetwork for short. In particular, partial singleton path-consistency has been shown to play a crucial role in tackling the minimal labeling problem of a qualitative constraint network, which is the problem of finding the strongest implied constraints of that network. In this paper, we propose a stronger local consistency that couples partial singleton path-consistency with the idea of collectively deleting certain unfeasible base relations by exploiting singleton checks. We then propose an efficient algorithm for enforcing this consistency that, given a qualitative constraint network, performs fewer constraint checks than the respective algorithm for enforcing partial singleton path-consistency in that network. We formally prove certain properties of our new local consistency, and motivate its usefulness through demonstrative examples and a preliminary experimental evaluation with qualitative constraint networks of Interval Algebra.
  • Qualitative constraint network
  • qualitative spatial and temporal reasoning
  • partial singleton path-consistency
  • local consistency
  • minimal labeling pr


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  1. James F. Allen. Maintaining Knowledge about Temporal Intervals. Commun. ACM, 26:832-843, 1983. URL:
  2. Nouhad Amaneddine, Jean-François Condotta, and Michael Sioutis. Efficient Approach to Solve the Minimal Labeling Problem of Temporal and Spatial Qualitative Constraints. In IJCAI, 2013. Google Scholar
  3. Philippe Balbiani, Jean-François Condotta, and Luis Fariñas del Cerro. Tractability Results in the Block Algebra. J. Log. Comput., 12:885-909, 2002. URL:
  4. Hachemi Bennaceur and Mohamed-Salah Affane. Partition-k-AC: An Efficient Filtering Technique Combining Domain Partition and Arc Consistency. In CP, 2001. Google Scholar
  5. Christian Bessière. Arc-Consistency and Arc-Consistency Again. Artif. Intell., 65:179-190, 1994. Google Scholar
  6. Mehul Bhatt, Hans W. Guesgen, Stefan Wölfl, and Shyamanta Moni Hazarika. Qualitative Spatial and Temporal Reasoning: Emerging Applications, Trends, and Directions. Spatial Cognition & Computation, 11:1-14, 2011. URL:
  7. Assef Chmeiss and Jean-François Condotta. Consistency of Triangulated Temporal Qualitative Constraint Networks. In ICTAI, 2011. URL:
  8. Jean-François Condotta and Christophe Lecoutre. A Class of df-Consistencies for Qualitative Constraint Networks. In KR, 2010. Google Scholar
  9. Romuald Debruyne and Christian Bessière. Some Practicable Filtering Techniques for the Constraint Satisfaction Problem. In IJCAI, 1997. Google Scholar
  10. Frank Dylla, Till Mossakowski, Thomas Schneider, and Diedrich Wolter. Algebraic Properties of Qualitative Spatio-Temporal Calculi. In COSIT, 2013. URL:
  11. Andrew U. Frank. Qualitative Spatial Reasoning with Cardinal Directions. In ÖGAI, 1991. Google Scholar
  12. Alfonso Gerevini. Incremental qualitative temporal reasoning: Algorithms for the Point Algebra and the ORD-Horn class. Artif. Intell., 166:37-80, 2005. URL:
  13. Martin Charles Golumbic and Ron Shamir. Complexity and Algorithms for Reasoning about Time: A Graph-Theoretic Approach. J. ACM, 40:1108-1133, 1993. URL:
  14. Jinbo Huang. Compactness and its implications for qualitative spatial and temporal reasoning. In KR, 2012. Google Scholar
  15. Jinbo Huang, Jason Jingshi Li, and Jochen Renz. Decomposition and tractability in qualitative spatial and temporal reasoning. Artif. Intell., 195:140-164, 2013. URL:
  16. Peter B. Ladkin and Alexander Reinefeld. Fast Algebraic Methods for Interval Constraint Problems. Ann. Math. Artif. Intell., 19:383-411, 1997. URL:
  17. Sanjiang Li, Zhiguo Long, Weiming Liu, Matt Duckham, and Alan Both. On redundant topological constraints. Artif. Intell., 225:51-76, 2015. URL:
  18. Gérard Ligozat. Reasoning about cardinal directions. J. Vis. Lang. Comput., 9:23-44, 1998. URL:
  19. Gérard Ligozat and Jochen Renz. What Is a Qualitative Calculus? A General Framework. In PRICAI, 2004. URL:
  20. Zhiguo Long and Sanjiang Li. On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi. In COSIT, 2015. URL:
  21. Zhiguo Long, Michael Sioutis, and Sanjiang Li. Efficient Path Consistency Algorithm for Large Qualitative Constraint Networks. In IJCAI, 2016. Google Scholar
  22. Carsten Lutz and Maja Milicic. A Tableau Algorithm for DLs with Concrete Domains and GCIs. J. Autom. Reasoning, 38:227-259, 2007. Google Scholar
  23. Bernhard Nebel. Solving Hard Qualitative Temporal Reasoning Problems: Evaluating the Efficiency of Using the ORD-Horn Class. Constraints, 1:175-190, 1997. URL:
  24. David A. Randell, Zhan Cui, and Anthony Cohn. A Spatial Logic Based on Regions & Connection. In KR, 1992. Google Scholar
  25. Jochen Renz. A Canonical Model of the Region Connection Calculus. J. Appl. Non-Classical Logics, 12:469-494, 2002. Google Scholar
  26. Jochen Renz and Gérard Ligozat. Weak Composition for Qualitative Spatial and Temporal Reasoning. In CP, 2005. URL:
  27. Jochen Renz and Bernhard Nebel. Efficient Methods for Qualitative Spatial Reasoning. J. Artif. Intell. Res., 15:289-318, 2001. URL:
  28. Jochen Renz and Bernhard Nebel. Qualitative Spatial Reasoning Using Constraint Calculi. In Handbook of Spatial Logics, pages 161-215. Springer, 2007. URL:
  29. Michael Sioutis, Jean-François Condotta, and Manolis Koubarakis. An Efficient Approach for Tackling Large Real World Qualitative Spatial Networks. Int. J. Artif. Intell. Tools, 25:1-33, 2016. Google Scholar
  30. Michael Sioutis, Sanjiang Li, and Jean-François Condotta. Efficiently Characterizing Non-Redundant Constraints in Large Real World Qualitative Spatial Networks. In IJCAI, 2015. Google Scholar
  31. Michael Sioutis, Yakoub Salhi, and Jean-François Condotta. Studying the use and effect of graph decomposition in qualitative spatial and temporal reasoning. Knowl. Eng. Rev., 32:e4, 2016. Google Scholar
  32. Robert E. Tarjan and Mihalis Yannakakis. Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs. SIAM J. Comput., 13:566-579, 1984. URL:
  33. Alfred Tarski. On the calculus of relations. J. Symb. Log., 6:73-89, 1941. URL:
  34. Peter van Beek and Dennis W. Manchak. The design and experimental analysis of algorithms for temporal reasoning. J. Artif. Intell. Res., 4:1-18, 1996. Google Scholar
  35. Marc B. Vilain and Henry A. Kautz. Constraint Propagation Algorithms for Temporal Reasoning. In AAAI, 1986. Google Scholar
  36. Richard J. Wallace. Neighbourhood SAC: Extensions and new algorithms. AI Commun., 29:249-268, 2016. URL:
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