Artificial Intelligence
Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Valuation-based systems: a framework for managing uncertainty in expert systems
Fuzzy logic for the management of uncertainty
Possibilistic constraint satisfaction problems or “how to handle soft constraints?”
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
Linear independence in bottleneck algebras
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Probabilistic Expert Systems
Local computation with valuations from a commutative semigroup
Annals of Mathematics and Artificial Intelligence
Mini-buckets: A general scheme for bounded inference
Journal of the ACM (JACM)
Branch and Bound with Mini-Bucket Heuristics
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
A General Scheme for Multiple Lower Bound Computation in Constraint Optimization
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Tree approximation for belief updating
Eighteenth national conference on Artificial intelligence
Information Algebras: Generic Structures for Inference
Information Algebras: Generic Structures for Inference
Properties of acyclic database schemes
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Arc consistency for soft constraints
Artificial Intelligence
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Unifying tree decompositions for reasoning in graphical models
Artificial Intelligence
Theory of Relational Databases
Theory of Relational Databases
Enhancing constraints manipulation in semiring-based formalisms
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Mini-buckets: a general scheme for generating approximations in automated reasoning
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Mini-bucket heuristics for improved search
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
The generalized distributive law
IEEE Transactions on Information Theory
Local Computation Schemes with Partially Ordered Preferences
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Semiring-induced propositional logic: definition and basic algorithms
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Generic solution construction in valuation-based systems
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
Bucket and mini-bucket schemes for m best solutions over graphical models
GKR'11 Proceedings of the Second international conference on Graph Structures for Knowledge Representation and Reasoning
Updating credal networks is approximable in polynomial time
International Journal of Approximate Reasoning
Semiring-based mini-bucket partitioning schemes
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Compositional models in valuation-based systems
International Journal of Approximate Reasoning
On a Condition for Semirings to Induce Compact Information Algebras
Electronic Notes in Theoretical Computer Science (ENTCS)
Hi-index | 0.01 |
Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra. There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.