A Decomposition Framework for Inconsistency Handling in Qualitative Spatial and Temporal Reasoning.

Decomposition can be a fundamental process for dealing with inconsistency in different domains. Among other things, it allows us to capture potential contexts, identify conflicting factors, restore consistency, and measure inconsistency. The aim of this paper is to explore the process of decomposition in qualitative spatial and temporal reasoning. We first study a problem that consists in decomposing the original inconsistent constraint network into the fewest possible consistent subnetworks (components) that share a given part. After establishing several interesting theoretical properties, such as providing bounds on the number of components in a decomposition, as well as computational complexity results, we propose two methods for solving this problem. The first method is based on a SAT encoding, while the second one corresponds to a greedy constraint-based algorithm, a variant of which involves the use of spanning trees to reduce the number of oracle calls. Secondly, we consider a version of the previous decomposition problem by focusing on maximizing the similarity between the decomposition components; the similarity in this context is represented by the common constraints among components. We then adapt our methods to solve this new problem. Thirdly, we propose two inconsistency measures that are based on our decomposition framework and show that they satisfy several desired properties. Finally, we provide implementations of our decomposition methods and perform an experimental evaluation.