On the Utility of Neighbourhood Singleton-Style Consistencies for Qualitative Constraint-Based Spatial and Temporal Reasoning

A singleton-style consistency is a local consistency that verifies if each base relation (atom) of each constraint of a qualitative constraint network ( QCN ) can serve as a support with respect to the closure of that network under a (naturally) weaker local consistency. This local consistency is essential for tackling fundamental reasoning problems associated with QCN s, such as the satisfiability checking or the minimal labeling problem, but can suffer from redundant constraint checks, especially when those checks occur far from where the pruning usually takes place. In this paper, we propose singleton-style consistencies that are applied just on the neighbourhood of a singleton-checked constraint instead of the whole network. We make a theoretical comparison with existing consistencies and consequently prove some properties of the new ones. In addition, we propose algorithms to enforce our consistencies, as well as parsimonious variants thereof, that are more efficient in practice than the state of the art. We make an experimental evaluation with random and structured QCN s of Interval Algebra in the phase transition region to demonstrate the potential of our approach.