A valuation-based language for expert systems
International Journal of Approximate Reasoning
Valuation-based systems: a framework for managing uncertainty in expert systems
Fuzzy logic for the management of uncertainty
Valuation-based systems for Bayesian decision analysis
Operations Research
Hypertree decompositions and tractable queries
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
The complexity of acyclic conjunctive queries
Journal of the ACM (JACM)
Probabilistic Expert Systems
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Local computation with valuations from a commutative semigroup
Annals of Mathematics and Artificial Intelligence
Conjunctive Query Containment Revisited
ICDT '97 Proceedings of the 6th International Conference on Database Theory
Logical Deduction Using the Local Computation Framework
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Information Algebras: Generic Structures for Inference
Information Algebras: Generic Structures for Inference
A comparison of structural CSP decomposition methods
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
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Many problems of artificial intelligence, or more generally, many problems of information processing, have a generic solution based on local computation on join trees or acyclic hypertrees. There are several variants of this method all based on the algebraic structure of valuation algebras. A strong requirement underlying this approach is that the elements of a problem decomposition form a join tree. Although it is always possible to construct covering join trees, if the requirement is originally not satisfied, it is not always possible or not efficient to extend the elements of the decomposition to the covering join tree. Therefore in this paper different variants of an axiomatic framework of valuation algebras are introduced which prove sufficient for local computation without the need of an extension of the factors of a decomposition. This framework covers the axiomatic system proposed by Shenoy and Shafer (1990) [1]. A particular emphasis is laid on the important special cases of idempotent algebras and algebras with some notion of division. It is shown that all well-known architectures for local computation like the Shenoy-Shafer architecture, Lauritzen-Spiegelhalter and HUGIN architectures may be adapted to this new framework. Further a new architecture for idempotent algebras is presented. As examples, in addition to the classical instances of valuation algebras, semiring-based valuation algebras, Gaussian potentials and the relational algebra are presented.