From Path-Consistency to Global Consistency in Temporal Qualitative Constraint Networks

Abstract

We study in this paper the problem of global consistency for qualitative constraints networks (QCNs) of the Point Algebra (PA) and the Interval Algebra (IA). In particular, we consider the subclass $\mathcal{S}_{\sf PA}$ corresponding to the set of relations of PA except the relations { ,=}, and the subclass $\mathcal{S}_{\sf IA}$ corresponding to pointizable relations of IA one can express by means of relations of $\mathcal{S}_{\sf PA}$. We prove that path-consistency implies global consistency for QCNs defined on these subclasses. Moreover, we show that with the subclasses corresponding to convex relations, there are unique greatest subclasses of PA and IA containing singleton relations satisfying this property.