Dynamic Branching in Qualitative Constraint Networks via Counting Local Models

Authors Michael Sioutis , Diedrich Wolter

Thumbnail PDF


  • Filesize: 0.61 MB
  • 15 pages

Document Identifiers

Author Details

Michael Sioutis
  • Faculty of Information Systems and Applied Computer Sciences, University of Bamberg, Germany
Diedrich Wolter
  • Faculty of Information Systems and Applied Computer Sciences, University of Bamberg, Germany

Cite AsGet BibTex

Michael Sioutis and Diedrich Wolter. Dynamic Branching in Qualitative Constraint Networks via Counting Local Models. In 27th International Symposium on Temporal Representation and Reasoning (TIME 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 178, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We introduce and evaluate dynamic branching strategies for solving Qualitative Constraint Networks (QCNs), which are networks that are mostly used to represent and reason about spatial and temporal information via the use of simple qualitative relations, e.g., a constraint can be "Task A is scheduled after or during Task C". In qualitative constraint-based reasoning, the state-of-the-art approach to tackle a given QCN consists in employing a backtracking algorithm, where the branching decisions during search are governed by the restrictiveness of the possible relations for a given constraint (e.g., after can be more restrictive than during). In the literature, that restrictiveness is defined a priori by means of static weights that are precomputed and associated with the relations of a given calculus, without any regard to the particulars of a given network instance of that calculus, such as its structure. In this paper, we address this limitation by proposing heuristics that dynamically associate a weight with a relation, based on the count of local models (or local scenarios) that the relation is involved with in a given QCN; these models are local in that they focus on triples of variables instead of the entire QCN. Therefore, our approach is adaptive and seeks to make branching decisions that preserve most of the solutions by determining what proportion of local solutions agree with that decision. Experimental results with a random and a structured dataset of QCNs of Interval Algebra show that it is possible to achieve up to 5 times better performance for structured instances, whilst maintaining non-negligible gains of around 20% for random ones.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Computing methodologies → Temporal reasoning
  • Computing methodologies → Spatial and physical reasoning
  • Qualitative constraints
  • spatial and temporal reasoning
  • counting local models
  • dynamic branching
  • adaptive algorithm


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. James F. Allen. Maintaining Knowledge about Temporal Intervals. Commun. ACM, 26(11):832-843, 1983. URL: https://doi.org/10.1145/182.358434.
  2. Albert-László Barabási and Réka Albert. Emergence of scaling in random networks. Science (New York, N.Y.), 286(5439):509-512, 1999. URL: https://doi.org/10.1126/science.286.5439.509.
  3. Davide Bresolin, Dario Della Monica, Angelo Montanari, Pietro Sala, and Guido Sciavicco. Decidability and complexity of the fragments of the modal logic of Allen’s relations over the rationals. Inf. Comput., 266:97-125, 2019. URL: https://doi.org/10.1016/j.ic.2019.02.002.
  4. Assef Chmeiss and Jean-Francois Condotta. Consistency of Triangulated Temporal Qualitative Constraint Networks. In ICTAI, pages 799-802, 2011. URL: https://doi.org/10.1109/ICTAI.2011.125.
  5. Zhan Cui, Anthony G. Cohn, and David A. Randell. Qualitative Simulation Based on a Logical Formalism of Space and Time. In AAAI, pages 679-684, 1992. URL: http://www.aaai.org/Library/AAAI/1992/aaai92-105.php.
  6. Daniel de Leng and Fredrik Heintz. Qualitative Spatio-Temporal Stream Reasoning with Unobservable Intertemporal Spatial Relations Using Landmarks. In AAAI, pages 957-963, 2016. URL: http://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12077.
  7. Rina Dechter. Constraint processing. Elsevier Morgan Kaufmann, 2003. Google Scholar
  8. Frank Dylla, Jae Hee Lee, Till Mossakowski, Thomas Schneider, André van Delden, Jasper van de Ven, and Diedrich Wolter. A Survey of Qualitative Spatial and Temporal Calculi: Algebraic and Computational Properties. ACM Comput. Surv., 50(1):7:1-7:39, 2017. URL: https://doi.org/10.1145/3038927.
  9. Frank Dylla, Till Mossakowski, Thomas Schneider, and Diedrich Wolter. Algebraic Properties of Qualitative Spatio-temporal Calculi. In COSIT, pages 516-536, 2013. URL: https://doi.org/10.1007/978-3-319-01790-7_28.
  10. Frank Dylla and Jan Oliver Wallgrün. Qualitative Spatial Reasoning with Conceptual Neighborhoods for Agent Control. J. Intell. Robotic Syst., 48(1):55-78, 2007. URL: https://doi.org/10.1007/s10846-006-9099-4.
  11. David Gabelaia, Roman Kontchakov, Ágnes Kurucz, Frank Wolter, and Michael Zakharyaschev. Combining Spatial and Temporal Logics: Expressiveness vs. Complexity. J. Artif. Intell. Res., 23:167-243, 2005. URL: https://doi.org/10.1613/jair.1537.
  12. Johann Gamper and Wolfgang Nejdl. Abstract temporal diagnosis in medical domains. Artificial Intelligence in Medicine, 10(3):209-234, 1997. URL: https://doi.org/10.1016/S0933-3657(97)00393-X.
  13. Zeno Gantner, Matthias Westphal, and Stefan Wölfl. GQR-A Fast Reasoner for Binary Qualitative Constraint Calculi. In AAAI Workshop on Spatial and Temporal Reasoning, 2008. Google Scholar
  14. Fredrik Heintz and Daniel de Leng. Spatio-Temporal Stream Reasoning with Incomplete Spatial Information. In ECAI, pages 429-434, 2014. URL: https://doi.org/10.3233/978-1-61499-419-0-429.
  15. Jinbo Huang. Compactness and its implications for qualitative spatial and temporal reasoning. In KR, 2012. Google Scholar
  16. Roman Kontchakov, Agi Kurucz, Frank Wolter, and Michael Zakharyaschev. Spatial Logic + Temporal Logic = ? In Handbook of Spatial Logics, pages 497-564. Springer-Verlag, 2007. URL: https://doi.org/10.1007/978-1-4020-5587-4_9.
  17. Nikhil Krishnaswamy, Scott Friedman, and James Pustejovsky. Combining Deep Learning and Qualitative Spatial Reasoning to Learn Complex Structures from Sparse Examples with Noise. In AAAI, pages 411-415, 2019. Google Scholar
  18. Gérard Ligozat. Qualitative Spatial and Temporal Reasoning. ISTE. Wiley, 2013. Google Scholar
  19. Gérard Ligozat and Jochen Renz. What Is a Qualitative Calculus? A General Framework. In PRICAI, pages 53-64, 2004. URL: https://doi.org/10.1007/978-3-540-28633-2_8.
  20. Antonio Morales, Isabel Navarrete, and Guido Sciavicco. A new modal logic for reasoning about space: spatial propositional neighborhood logic. Ann. Math. Artif. Intell., 51(1):1-25, 2007. URL: https://doi.org/10.1007/s10472-007-9083-0.
  21. Emilio Muñoz-Velasco, Mercedes Pelegrín-García, Pietro Sala, Guido Sciavicco, and Ionel Eduard Stan. On coarser interval temporal logics. Artif. Intell., 266:1-26, 2019. URL: https://doi.org/10.1016/j.artint.2018.09.001.
  22. Bernhard Nebel. Solving Hard Qualitative Temporal Reasoning Problems: Evaluating the Efficiency of Using the ORD-Horn Class. Constraints, 1(3):175-190, 1997. URL: https://doi.org/10.1007/BF00137869.
  23. Bernhard Nebel and Hans-Jürgen Bürckert. Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen’s Interval Algebra. J. ACM, 42(1):43-66, 1995. URL: https://doi.org/10.1145/200836.200848.
  24. Gilles Pesant, Claude-Guy Quimper, and Alessandro Zanarini. Counting-Based Search: Branching Heuristics for Constraint Satisfaction Problems. J. Artif. Intell. Res., 43:173-210, 2012. URL: https://doi.org/10.1613/jair.3463.
  25. David A. Randell, Zhan Cui, and Anthony Cohn. A Spatial Logic Based on Regions and Connection. In KR, pages 165-176, 1992. Google Scholar
  26. Jochen Renz. Qualitative Spatial and Temporal Reasoning: Efficient Algorithms for Everyone. In IJCAI, pages 526-531, 2007. Google Scholar
  27. Jochen Renz and Gérard Ligozat. Weak Composition for Qualitative Spatial and Temporal Reasoning. In CP, pages 534-548, 2005. URL: https://doi.org/10.1007/11564751_40.
  28. Jochen Renz and Bernhard Nebel. Efficient Methods for Qualitative Spatial Reasoning. J. Artif. Intell. Res., 15:289-318, 2001. URL: https://doi.org/10.1613/jair.872.
  29. Jochen Renz and Bernhard Nebel. Qualitative Spatial Reasoning Using Constraint Calculi. In Handbook of Spatial Logics, pages 161-215. Springer-Verlag, 2007. URL: https://doi.org/10.1007/978-1-4020-5587-4_4.
  30. Michael Sioutis. Just-In-Time Constraint-Based Inference for Qualitative Spatial and Temporal Reasoning. KI, 34(2):259-270, 2020. URL: https://doi.org/10.1007/s13218-020-00652-z.
  31. 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. URL: https://doi.org/10.1142/S0218213015500311.
  32. Michael Sioutis, Zhiguo Long, and Tomi Janhunen. On Robustness in Qualitative Constraint Networks. In IJCAI, pages 448-455, 2020. To appear. Google Scholar
  33. Michael Sioutis, Anastasia Paparrizou, and Jean-François Condotta. Collective singleton-based consistency for qualitative constraint networks: Theory and practice. Theor. Comput. Sci., 797:17-41, 2019. URL: https://doi.org/10.1016/j.tcs.2019.02.028.
  34. 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, 2017. URL: https://doi.org/10.1017/S026988891600014X.
  35. Jakob Suchan and Mehul Bhatt. Semantic Question-Answering with Video and Eye-Tracking Data: AI Foundations for Human Visual Perception Driven Cognitive Film Studies. In IJCAI, pages 2633-2639, 2016. URL: http://www.ijcai.org/Abstract/16/374.
  36. Jakob Suchan, Mehul Bhatt, and Srikrishna Varadarajan. Out of Sight But Not Out of Mind: An Answer Set Programming Based Online Abduction Framework for Visual Sensemaking in Autonomous Driving. In IJCAI, pages 1879-1885, 2019. URL: https://doi.org/10.24963/ijcai.2019/260.
  37. Jakob Suchan, Mehul Bhatt, Przemyslaw Andrzej Walega, and Carl P. L. Schultz. Visual Explanation by High-Level Abduction: On Answer-Set Programming Driven Reasoning About Moving Objects. In AAAI, pages 1965-1972, 2018. URL: https://www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/17303.
  38. 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(3):566-579, 1984. URL: https://doi.org/10.1137/0213035.
  39. Peter van Beek and Dennis W. Manchak. The design and experimental analysis of algorithms for temporal reasoning. J. Artif. Intell. Res., 4(1):1-18, 1996. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail