Information Algebras

Generic Structures For Inference
Softcover Nachdruck of the original 1. Auflage 2003
ISBN: 978-1-85233-689-9
Verlag: Springer

Buch, Englisch, 265 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 429 g

Reihe: Discrete Mathematics and Theoretical Computer Science

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.

Zielgruppe

Research

Autoren/Hrsg.

Kohlas, Juerg

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Wissensbasierte Systeme, Expertensysteme
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen

Inhaltsverzeichnis

1 Introduction.- 2 Valuation Algebras.- 2.1 The Framework.- 2.2 Axioms.- 2.3 Examples of Valuation Algebras.- 2.4 Partial Marginalization.- 3 Algebraic Theory.- 3.1 Congruences.- 3.2 Domain-Free Valuation Algebras.- 3.3 Subalgebras, Homomorphisms.- 3.4 Null Valuations.- 3.5 Regular Valuation Algebras.- 3.6 Separative Valuation Algebras.- 3.7 Scaled Valuation Algebras.- 4 Local Computation.- 4.1 Fusion Algorithm.- 4.2 Collect Algorithm.- 4.3 Computing Multiple Marginals.- 4.4 Architectures with Division.- 4.5 Computations in Valuation Algebras with Partial Marginalization.- 4.6 Scaling and Updating.- 5 Conditional Independence.- 5.1 Factorization and Graphical Models.- 5.2 Conditionals in Regular Algebras.- 5.3 Conditionals in Separative Algebras.- 6 Information Algebras.- 6.1 Idempotency.- 6.2 Partial Order of Information.- 6.3 File Systems.- 6.4 Information Systems.- 6.5 Examples.- 6.6 Compact Systems.- 6.7 Mappings.- 7 Uncertain Information.- 7.1 Algebra of Random Variables.- 7.2 Probabilistic Argumentation Systems.- 7.3 Allocations of Probability.- 7.4 Independent Sources.- References.