Constraint Hierarchies as Semiring-Based CSPs

Constraints provide an effective means for the high-level modeling and reasoning of various problems. In particular, soft constraints are useful since they treat over-constrained problems that naturally arise in real-life applications. Therefore, researchers have been exploring frameworks for soft constraints. The framework of semiring-based constraint satisfaction problems (CSPs) can express many kinds of soft constraints such as weighted CSPs and fuzzy CSPs. The framework of constraint hierarchies emphasizes hierarchical preferences of soft constraints. Although semiring-based CSPs are known to be considerably general, it has been unclear whether they can express constraint hierarchies. In this paper, we show that a reasonable class of constraint hierarchies can be regarded as an instance of semiring-based CSPs.