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The Horn Fragment of Branching Algebra

Authors Alessandro Bertagnon , Marco Gavanelli , Alessandro Passantino , Guido Sciavicco , Stefano Trevisani

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Author Details

Alessandro Bertagnon
  • Department of Engineering, University of Ferrara, Italy
Marco Gavanelli
  • Department of Engineering, University of Ferrara, Italy
Alessandro Passantino
  • Department of Mathematics and Computer Science, University of Ferrara, Italy
Guido Sciavicco
  • Department of Mathematics and Computer Science, University of Ferrara, Italy
Stefano Trevisani
  • Department of Mathematics and Computer Science, University of Ferrara, Italy

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Alessandro Bertagnon, Marco Gavanelli, Alessandro Passantino, Guido Sciavicco, and Stefano Trevisani. The Horn Fragment of Branching Algebra. In 27th International Symposium on Temporal Representation and Reasoning (TIME 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 178, pp. 5:1-5:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


Branching Algebra is the natural branching-time generalization of Allen’s Interval Algebra. As in the linear case, the consistency problem for Branching Algebra is NP-hard. Being relatively new, however, not much is known about the computational behaviour of the consistency problem of its sub-algebras, except in the case of the recently found subset of convex branching relations, for which the consistency of a network can be tested via path consistency and it is therefore deterministic polynomial. In this paper, following Nebel and Bürckert, we define the Horn fragment of Branching Algebra, and prove that it is a sub-algebra of the latter, being closed under inverse, intersection, and composition, that it strictly contains both the convex fragment of Branching Algebra and the Horn fragment of Interval Algebra, and that its consistency problem can be decided via path consistency. Finally, we experimentally prove that the Horn fragment of Branching Algebra can be used as an heuristic for checking the consistency of a generic network with a considerable improvement over the convex subset.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Constraint programming
  • Consistency
  • Branching time
  • Horn Fragment


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