Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Valuation-based systems for discrete optimisation
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Preference-based search and multi-criteria optimization
Eighteenth national conference on Artificial intelligence
Information Algebras: Generic Structures for Inference
Information Algebras: Generic Structures for Inference
Arc consistency for soft constraints
Artificial Intelligence
Bucket elimination for multiobjective optimization problems
Journal of Heuristics
Semiring induced valuation algebras: Exact and approximate local computation algorithms
Artificial Intelligence
Algebraic Structures for Bipolar Constraint-Based Reasoning
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Preferred subtheories: an extended logical framework for default reasoning
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Constraint solving over semirings
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Plausibility measures and default reasoning
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
An order of magnitude calculus
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Decision making with multiple objectives using GAI networks
Artificial Intelligence
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Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A major strength of this work is that it is based on an algebraic description: what is proved is the correctness of the local computation algorithm under a few axioms on the algebraic structure. The instantiations of the framework in practice make use of totally ordered scales. The present paper focuses on the use of partially ordered scales and examines how such scales can be cast in the Shafer-Shenoy framework and thus benefit from local computation algorithms. It also provides many examples of such scales, thus showing that each of the algebraic structures explored here is of interest.