Consistency of Qualitative Constraint Networks from Tree Decompositions

A common way to decide the consistency problem of a qualitative constraint network (QCN) is to encode it as a boolean formula in order to benefit from the efficiency of SAT solvers. In recent works, a decomposition method of QCNs have been proposed to reduce the amount of boolean formulae. In this paper, we first show that the decompositions used can be expressed by particular tree decompositions. Furthermore, for some classes of relations, we prove that the consistency problem of a QCN can be decided by applying the method of the closure by weak composition on the clusters of a tree decomposition. This result allows us to extend the approach recently proposed to tree decompositions of QCNs.