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**Computation in valuation algebras.**
*(English)*
Zbl 1015.68196

Gabbay, Dov M. (ed.) et al., Handbook of defeasible reasoning and uncertainty management systems. Vol. 5: Algorithms for uncertainty and defeasible reasoning. Dordrecht: Kluwer Academic Publishers. 5-39 (2000).

Summary: The main goal of this chapter is to describe an abstract framework called valuation algebra for computing marginals using local computation. The valuation algebra framework is useful in many domains, and especially for managing uncertainty in expert systems using probability, Dempster-Shafer belief functions, Spohnian epistemic belief theory, and possibility theory.

An outline of the chapter is as follows. Section 2 introduces valuation algebras. Section 3 describes the fusion algorithm for computing a marginal. Sections 4 and 5 present different computational architectures, namely Shafer-Shenoy architecture, Lauritzen-Spiegelhalter architecture, and HUGIN architecture. The latter two systems depend on an additional concept, called continuers (or alternatively division). Continuation is introduced in section 5. Examples of abstract computation are dispersed in the different sections. Section 6 finally mentions some further examples of abstract computation.

For the entire collection see [Zbl 0959.00013].

An outline of the chapter is as follows. Section 2 introduces valuation algebras. Section 3 describes the fusion algorithm for computing a marginal. Sections 4 and 5 present different computational architectures, namely Shafer-Shenoy architecture, Lauritzen-Spiegelhalter architecture, and HUGIN architecture. The latter two systems depend on an additional concept, called continuers (or alternatively division). Continuation is introduced in section 5. Examples of abstract computation are dispersed in the different sections. Section 6 finally mentions some further examples of abstract computation.

For the entire collection see [Zbl 0959.00013].

### MSC:

68T35 | Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence |