Information Algebras : Generic Structures For Inference - Juerg Kohlas

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Information Algebras

Generic Structures For Inference

By: Juerg Kohlas

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Paperback | 5 December 2002

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280 Pages

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23.5 x 15.88 x 1.27

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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.

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You Can Find This Book In

Non-Fiction Mathematics Algebra Reference, Information & Interdisciplinary Subjects Research & Information Information theory Computing & I.T.Computer Science Artificial Intelligence Probability & Statistics Computer Programming & Software Development Algorithms & Data Structures

Mathematical Theory of Computation Gardening

Introduction	p. 1
Valuation Algebras	p. 7
The Framework	p. 7
Axioms	p. 11
Examples of Valuation Algebras	p. 16
Partial Marginalization	p. 37
Algebraic Theory	p. 41
Congruences	p. 41
Domain-Free Valuation Algebras	p. 49
Subalgebras, Homomorphisms	p. 55
Null Valuations	p. 64
Regular Valuation Algebras	p. 67
Separative Valuation Algebras	p. 78
Scaled Valuation Algebras	p. 89
Local Computation	p. 95
Fusion Algorithm	p. 95
Collect Algorithm	p. 103
Computing Multiple Marginals	p. 108
Architectures with Division	p. 111
Computations in Valuation Algebras with Partial Marginalization	p. 119
Scaling and Updating	p. 124
Conditional Independence	p. 131
Factorization and Graphical Models	p. 131
Conditionals in Regular Algebras	p. 141
Conditionals in Separative Algebras	p. 150
Information Algebras	p. 159
Idempotency	p. 159
Partial Order of Information	p. 163
File Systems	p. 169
Information Systems	p. 176
Examples	p. 185
Compact Systems	p. 192
Mappings	p. 201
Uncertain Information	p. 209
Algebra of Random Variables	p. 209
Probabilistic Argumentation Systems	p. 218
Allocations of Probability	p. 227
Independent Sources	p. 245
References	p. 251
Index	p. 257
Table of Contents provided by Blackwell. All Rights Reserved.

Information Algebras

Generic Structures For Inference

At a Glance

Paperback

Shipping

How to return your order

Defective items

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