Constraint-Based Inference (CBI) is a unified framework that subsumes many practical problems in different research communities. These problems include probabilistic inference, decision-making under uncertainty, constraint satisfaction, propositional satisfiability, decoding problems, and possibility inference. Recently, researchers have presented various unified representation and algorithmic frameworks for CBI problems in their fields, based on the increasing awareness that these problems share common features in representation and essentially identical inference approaches. As the first contribution of this paper, we explicitly use the semiring concept to generalize various CBI problems into a single formal representation framework that provides a broader coverage of the problem space based on the synthesis of existing generalized frameworks. Second, the proposed semiring-based unified framework is also a single formal algorithmic framework that provides a broader coverage of both exact and approximate inference algorithms, including variable elimination, junction tree, and loopy message propagation methods. Third, we discuss inference algorithm design and complexity issues. Finally, we present a software toolkit named the Generalized Constraint-Based Inference Toolkit in Java (GCBIJ) as the last contribution of this paper. GCBIJ is the first concrete software toolkit that implements the abstract semiring approach to unify the CBI problem representations and the inference algorithms. The discussion and the experimental results based on GCBIJ show that the generalized CBI framework is a useful tool for both research and applications.
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