A valuation-based language for expert systems
International Journal of Approximate Reasoning
On Spohn's rule for revision of beliefs
International Journal of Approximate Reasoning
Valuation-based systems for propositional logic
Methodologies for intelligent systems, 5
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
Nonserial Dynamic Programming
Local computation with valuations from a commutative semigroup
Annals of Mathematics and Artificial Intelligence
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
Information Algebras: Generic Structures for Inference
Information Algebras: Generic Structures for Inference
Semiring induced valuation algebras: Exact and approximate local computation algorithms
Artificial Intelligence
Probabilistic Conditional Independence Structures
Probabilistic Conditional Independence Structures
Characteristic properties of equivalent structures in compositional models
International Journal of Approximate Reasoning
Generic Inference: A Unifying Theory for Automated Reasoning
Generic Inference: A Unifying Theory for Automated Reasoning
A method for implementing a probabilistic model as a relational database
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Composition of probability measures on finite spaces
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Local computations in Dempster--Shafer theory of evidence
International Journal of Approximate Reasoning
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Compositional models were initially described for discrete probability theory, and later extended for possibility theory and for belief functions in Dempster-Shafer (D-S) theory of evidence. Valuation-based system (VBS) is an unifying theoretical framework generalizing some of the well known and frequently used uncertainty calculi. This generalization enables us to not only highlight the most important theoretical properties necessary for efficient inference (analogous to Bayesian inference in the framework of Bayesian network), but also to design efficient computational procedures. Some of the specific calculi covered by VBS are probability theory, a version of possibility theory where combination is the product t-norm, Spohn's epistemic belief theory, and D-S belief function theory. In this paper, we describe compositional models in the general framework of VBS using the semantics of no-double counting, which is central to the VBS framework. Also, we show that conditioning can be expressed using the composition operator. We define a special case of compositional models called decomposable models, again in the VBS framework, and demonstrate that for the class of decomposable compositional models, conditioning can be done using local computation. As all results are obtained for the VBS framework, they hold in all calculi that fit in the VBS framework. For the D-S theory of belief functions, the compositional model defined here differs from the one studied by Jirousek, Vejnarova, and Daniel. The latter model can also be described in the VBS framework, but with a combination operator that is different from Dempster's rule of combination. For the version of possibility theory in which combination is the product t-norm, the compositional model defined here reduces to the one studied by Vejnarova.