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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) https://doi.org/10.4230/LIPIcs.TIME.2017.19

Abstract

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.

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Keywords
  • Qualitative constraint network
  • qualitative spatial and temporal reasoning
  • partial singleton path-consistency
  • local consistency
  • minimal labeling pr

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