Finite Model Theory and Its Applications
by
Erich Graedel, Phokion G. Kolaitis, Leonid Libkin, Maarten Marx,
Joel Spencer, Moshe Y. Vardi, Yde Venema, and Scott Weinstein

Springer, 2007, 437 pages, hardcover,
ISBN: 978-3-540-00428-8.
(Series: Texts in Theoretical Computer Science. An EATCS Series)

From the back cover: This book gives a comprehensive overview of central
topics in finite model theory - expressive power of logics, descriptive
complexity, and zero-one laws - together with selected applications
relating to database theory and artificial intelligence, especially
constraint databases and constraint satisfaction problems. The final
chapter provides a concise modern introduction to modal logic,
emphasizing the interaction with finite model theory. The underlying
theme of the book is the use of  first-order, second-order, fixed-point,
and infinitary logic, as well as various fragments of and hierarchies
within these logics, to gain insight into phenomena and problems in
complexity theory and combinatorics.

The book emphasizes the use of combinatorial games, such as extensions
and refinements of the Ehrenfeucht-Fraissi games, as a powerful way to
analyze the expressive power of logics, and illustrates how sophisticated
notions from model theory and combinatorics, such as o-minimality and
treewidth, arise naturally in the applications of finite model theory
to database theory and artificial intelligence.

Students of logic and computer science will find here the tools
necessary to embark on research into finite model theory, and all
readers will experience the excitement of a vibrant area of the
applications of logic to computer science.

Table of contents:
1.Unifying Themes in Finite Model Theory
2.On the Expressive Power of Logics on Finite Models
3.Finite Model Theory and Descriptive Complexity
4.Logic and Random Structures
5.Embedded Finite Models and Constraint Databases
6.A Logical Approach to Constraint Satisfaction
7.Local Variations on a Loose Theme: Modal Logic and Decidability

To order, see http://www.springer.com/978-3-540-00428-8