Finite Model Theory and Its Applications

  • Erich Grädel
  • Phokion G. Kolaitis
  • Leonid Libkin
  • Maarten Marx
  • Joel Spencer
  • Moshe Y. Vardi
  • Yde Venema
  • Scott Weinstein

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Scott Weinstein
    Pages 1-25
  3. Phokion G. Kolaitis
    Pages 27-123
  4. Joel Spencer
    Pages 231-256
  5. Phokion G. Kolaitis, Moshe Y. Vardi
    Pages 339-370
  6. Back Matter
    Pages 431-437

About this book

Introduction

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.

Keywords

artificial intelligence complexity complexity theory computer computer science database logic

Authors and affiliations

  • Erich Grädel
    • 1
  • Phokion G. Kolaitis
    • 2
  • Leonid Libkin
    • 3
  • Maarten Marx
    • 4
  • Joel Spencer
    • 5
  • Moshe Y. Vardi
    • 6
  • Yde Venema
    • 7
  • Scott Weinstein
    • 8
  1. 1.Mathematical Foundations of Computer ScienceRWTH AachenAachen
  2. 2.IBM Almaden Research CenterUniv. of California at Santa Cruz
  3. 3.Univ. of Edinburgh
  4. 4.ISLA, Universiteit van AmsterdamAmsterdam
  5. 5.Courant InstituteNew York
  6. 6.Rice UniversityHouston
  7. 7.Universiteit van AmsterdamAmsterdam
  8. 8.Univ. of Pennsylvania

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-68804-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-540-00428-8
  • Online ISBN 978-3-540-68804-4
  • Series Print ISSN 1862-4499
  • About this book