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dc.contributor.authorKohlas, Jürg
dc.contributor.authorShenoy, Prakash P.
dc.date.accessioned2004-12-17T22:57:01Z
dc.date.available2004-12-17T22:57:01Z
dc.date.issued2000
dc.identifier.citationKohlas, J. and P. P. Shenoy, "Computation in Valuation Algebras," in D. M. Gabbay and P. Smets (eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems: Algorithms for Uncertainty and Defeasible Reasoning, Vol. 5, pp. 5--39, Kluwer Academic Publishers, Dordrecht.
dc.identifier.isbn0-7923-6672-7
dc.identifier.urihttp://hdl.handle.net/1808/165
dc.description.abstractMany different formalisms for treating uncertainty or, more generally, information and knowledge, have a common underlying algebraic structure. The essential algebraic operations are combination, which corresponds to aggregation of knowledge, and marginalization, which corresponds to focusing of knowledge. This structure is called a valuation algebra. Besides managing uncertainty in expert systems, valuation algebras can also be used to to represent constraint satisfaction problems, propositional logic, and discrete optimization problems. This chapter presents an axiomatic approach to valuation algebras. Based on this algebraic structure, different inference mechanisms that use local computations are described. These include the fusion algorithm and, derived from it, the Shenoy-Shafer architecture. As a particular case, computation in idempotent valuation algebras, also called information algebras, is discussed. The additional notion of continuers is introduced and, based on it, two more computational architectures, the Lauritzen-Spiegelhalter and the HUGIN architecture, are presented. Finally, different models of valuation algebras are considered. These include probability functions, Dempster-Shafer belief functions, Spohnian disbelief functions, and possibility functions. As further examples, linear manifolds and systems of linear equations, convex polyhedra and linear inequalities, propositional logic and information systems, and discrete optimization are mentioned.
dc.format.extent317185 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherKluwer Academic Publishers
dc.relation.ispartofseriesHandbook of Defeasible Reasoning and Uncertainty Management Systems;Vol. 5
dc.subjectValuation networks
dc.subjectValuation-based systems
dc.subjectLocal computation
dc.titleComputation in Valuation Algebras
dc.typeBook chapter
kusw.oastatusna
dc.identifier.orcidhttps://orcid.org/0000-0002-8425-896X
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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