Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Axioms for probability and belief-function propagation
Readings in uncertain reasoning
Valuation-based systems: a framework for managing uncertainty in expert systems
Fuzzy logic for the management of uncertainty
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Information Algebras: Generic Structures for Inference
Information Algebras: Generic Structures for Inference
Constraint Processing
Algebraic Structures for Transitive Closure
Algebraic Structures for Transitive Closure
Semiring induced valuation algebras: Exact and approximate local computation algorithms
Artificial Intelligence
Generic Inference: A Unifying Theory for Automated Reasoning
Generic Inference: A Unifying Theory for Automated Reasoning
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Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notions of solutions. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to linear equation systems. Contrary to inference, there is no general algorithm to compute solutions in arbitrary valuation algebras. This paper states formal requirements for the presence of solutions and proposes a generic algorithm for solution construction based on the results of a previously executed inference scheme. We study the application of generic solution construction to semiring constraint systems, sparse linear systems and algebraic path problems and show that the proposed method generalizes various existing approaches for specific formalisms in the literature.