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Information Algebras

Generic Structures For Inference

  • Book
  • © 2003

Overview

Authors:
  1. Jürg Kohlas

    1. Department of Informatics, University of Fribourg, Fribourg, Switzerland

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  • For the first time the common, abstract and unifying algebraic structure underlying different inference algorithms as used in Bayesian networks, possibility theory, Dempster-Shafer theory, logic, linear systems (sparse matrices) is presented in book form
  • Includes supplementary material: sn.pub/extras

Part of the book series: Discrete Mathematics and Theoretical Computer Science (DISCMATH)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Jürg Kohlas
    Pages 1-6

  3. Valuation Algebras

    • Jürg Kohlas
    Pages 7-40

  4. Algebraic Theory

    • Jürg Kohlas
    Pages 41-94

  5. Local Computation

    • Jürg Kohlas
    Pages 95-129

  6. Conditional Independence

    • Jürg Kohlas
    Pages 131-158

  7. Information Algebras

    • Jürg Kohlas
    Pages 159-207

  8. Uncertain Information

    • Jürg Kohlas
    Pages 209-250

  9. Back Matter

    Pages 251-266
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Keywords

About this book

Information usually comes in pieces, from different sources. It refers to different, but related questions. Therefore information needs to be aggregated and focused onto the relevant questions. Considering combination and focusing of information as the relevant operations leads to a generic algebraic structure for information. This book introduces and studies information from this algebraic point of view. Algebras of information provide the necessary abstract framework for generic inference procedures. They allow the application of these procedures to a large variety of different formalisms for representing information. At the same time they permit a generic study of conditional independence, a property considered as fundamental for knowledge presentation. Information algebras provide a natural framework to define and study uncertain information. Uncertain information is represented by random variables that naturally form information algebras. This theory also relates to probabilistic assumption-based reasoning in information systems and is the basis for the belief functions in the Dempster-Shafer theory of evidence.

Authors and Affiliations

  • Department of Informatics, University of Fribourg, Fribourg, Switzerland

    Jürg Kohlas

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