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Finite Model Theory and Its Applications.

Author: W Brauer; J Hromkovic; G Rozenberg
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
Series: Texts in Theoretical Computer Science an EATCS Series
Edition/Format:   eBook : Document : English
Summary:
This book gives a broad overview of core topics of finite model theory: expressive power, descriptive complexity, and zero-one laws, together with selected applications to database theory and artificial intelligence, especially, constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, which emphasizes the continuity in spirit and technique  Read more...
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Details

Genre/Form: Electronic books
Material Type: Document
Document Type: Book, Computer File
All Authors / Contributors: W Brauer; J Hromkovic; G Rozenberg
ISBN: 3540004289 9783540004288
OCLC Number: 990732692
Language Note: English.
Description: 1 online resource (446 pages).
Contents: Unifying Themes in Finite Model Theory --
On the Expressive Power of Logics on Finite Models --
Finite Model Theory and Descriptive Complexity --
Logic and Random Structures --
Embedded Finite Models and Constraint Databases --
A Logical Approach to Constraint Satisfaction --
Local Variations on a Loose Theme: Modal Logic and Decidability.
Series Title: Texts in Theoretical Computer Science an EATCS Series
Other Titles: Texts in Theoretical Computer Science an EATCS Series

Abstract:

This book gives a broad overview of core topics of finite model theory: expressive power, descriptive complexity, and zero-one laws, together with selected applications to database theory and artificial intelligence, especially, constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, which emphasizes the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of, and hierarchies within, first order, second order, fixed point, and infinitary logics to gain insight into phenomena in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful technique for analyzing the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and tree-width, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research in finite model theory, and all readers will experience the excitement of a vibrant area of application of logic to computer science.

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