Arc consistency and generalized arc consistency are two of the most important local consistency techniques for binary and non-binary classic constraint satisfaction problems (CSPs). Based on the Semiring CSP and Valued CSP frameworks, arc consistency has also been extended to handle soft constraint satisfaction problems such as fuzzy CSP, probabilistic CSP, max CSP, and weighted CSP. This extension is based on an idempotent or strictly monotonic constraint combination operator. In this paper, we present a weaker condition for applying the generalized arc consistency approach to constraint-based inference problems other than classic and soft CSPs. These problems, including probability inference and maximal likelihood decoding, can be processed using generalized arc consistency enforcing approaches. We also show that, given an additional monotonic condition on the corresponding semiring structure, some of constraint-based inference problems can be approximately preprocessed using generalized arc consistency algorithms.
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