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    Computation in Valuation Algebras

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    DRUMS.pdf (309.7Kb)
    Issue Date
    2000
    Author
    Kohlas, Jürg
    Shenoy, Prakash P.
    Publisher
    Kluwer Academic Publishers
    Format
    317185 bytes
    Type
    Book chapter
    Is part of series
    Handbook of Defeasible Reasoning and Uncertainty Management Systems;Vol. 5
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    Abstract
    Many 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.
    URI
    http://hdl.handle.net/1808/165
    ISBN
    0-7923-6672-7
    Collections
    • Distinguished Professors Scholarly Works [918]
    • School of Business Scholarly Works [213]
    Citation
    Kohlas, 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.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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