Deciding the Consistency of Branching Time Interval Networks

Authors Marco Gavanelli , Alessandro Passantino, Guido Sciavicco

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Author Details

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

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Marco Gavanelli, Alessandro Passantino, and Guido Sciavicco. Deciding the Consistency of Branching Time Interval Networks. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Allen's Interval Algebra (IA) is one of the most prominent formalisms in the area of qualitative temporal reasoning; however, its applications are naturally restricted to linear flows of time. When dealing with nonlinear time, Allen's algebra can be extended in several ways, and, as suggested by Ragni and Wölfl [M. Ragni and S. Wölfl, 2004], a possible solution consists in defining the Branching Algebra (BA) as a set of 19 basic relations (13 basic linear relations plus 6 new basic nonlinear ones) in such a way that each basic relation between two intervals is completely defined by the relative position of the endpoints on a tree-like partial order. While the problem of deciding the consistency of a network of IA-constraints is well-studied, and every subset of the IA has been classified with respect to the tractability of its consistency problem, the fragments of the BA have received less attention. In this paper, we first define the notion of convex BA-relation, and, then, we prove that the consistency of a network of convex BA-relations can be decided via path consistency, and is therefore a polynomial problem. This is the first non-trivial tractable fragment of the BA; given the clear parallel with the linear case, our contribution poses the bases for a deeper study of fragments of BA towards their complete classification.

Subject Classification

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


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