Elements of Finite Model Theory (Texts in Theoretical Computer Science. An EATCS Series) - Hardcover

Libkin, Leonid

Hardcover

ISBN 10: 3540212027 ISBN 13: 9783540212027

Publisher: Springer, 2004

Synopsis

Finite model theory is an area of mathematical logic that grew out of computer science applications. The main sources of motivational examples for finite model theory are found in database theory, computational complexity, and formal languages, although in recent years connections with other areas, such as formal methods and verification, and artificial intelligence, have been discovered. The birth of finite model theory is often identified with Trakhtenbrot's result from 1950 stating that validity over finite models is not recursively enumerable; in other words, completeness fails over finite models. The tech­ nique of the proof, based on encoding Turing machine computations as finite structures, was reused by Fagin almost a quarter century later to prove his cel­ ebrated result that put the equality sign between the class NP and existential second-order logic, thereby providing a machine-independent characterization of an important complexity class. In 1982, Immerman and Vardi showed that over ordered structures, a fixed point extension of first-order logic captures the complexity class PTIME of polynomial time computable propertiE~s. Shortly thereafter, logical characterizations of other important complexity classes were obtained. This line of work is often referred to as descriptive complexity. A different line of finite model theory research is associated with the de­ velopment of relational databases. By the late 1970s, the relational database model had replaced others, and all the basic query languages for it were es­ sentially first-order predicate calculus or its minor extensions.

About this title

About the Author

The author has been with the department of computer science at the University of Toronto since 2000. Prior to that, he was a researcher at Bell Laboratories, and he spent two years visiting INRIA in France. His research interests are in the areas of database theory and applications of logic in computer science.

He is coauthor/editor of:

Constraint Databases
Kuper, G., Libkin, L., Paredaens, J. (Eds.), 12.04.2000, ISBN 3-540-66151-4

Finite-Model Theory and Its Applications
Grädel, E., Kolaitis, P.G. (et al.), 07.2004, ISBN 3-540-00428-9

Semantics in Databases
Thalheim, B., Libkin, L. (Eds.), Vol. 1358, 25.02.1998, ISBN 3-540-64199-8

From the Back Cover

This book is an introduction to finite model theory which stresses the computer science origins of the area. In addition to presenting the main techniques for analyzing logics over finite models, the book deals extensively with applications in databases, complexity theory, and formal languages, as well as other branches of computer science. It covers Ehrenfeucht-Fraïssé games, locality-based techniques, complexity analysis of logics, including the basics of descriptive complexity, second-order logic and its fragments, connections with finite automata, fixed point logics, finite variable logics, zero-one laws, and embedded finite models, and gives a brief tour of recently discovered applications of finite model theory.

This book can be used both as an introduction to the subject, suitable for a one- or two-semester graduate course, or as reference for researchers who apply techniques from logic in computer science.

Edition details

• Publisher: Springer
• Publication date: 2004
• Language: English
• ISBN 10: 3540212027
• ISBN 13: 9783540212027
• Binding: Hardcover
• Number of pages: 332