Valuation Algebras
Marc Pouly, Jürg Kohlas · 2011
This chapter introduces the valuation algebra framework. Valuations can be imagined as pieces of information that refer to a question called the domain of the valuation. This domain is returned by the labeling operation. Two further operations called combination and projection are used to manipulate valuations. Combination corresponds to aggregation, and projection to focusing or extraction of knowledge. In addition, the valuation algebra framework consists of a set of six axioms that determine the behaviour of the three operations. Formalisms that satisfy the structure of valuation algebra are called instances and occur numerously in very different fields of mathematics and computer science. The chapter gives a first selection of instances including crisp constraints, arithmetic and probability potentials, Dempster-Shafer belief functions, density functions and the important family of Gaussian distributions. Controlled Vocabulary Terms probability