Finite Model Theory and Its Applications by Erich GrädelFinite Model Theory and Its Applications by Erich Grädel

Finite Model Theory and Its Applications

byErich Grädel, Phokion G. Kolaitis, Leonid Libkin

Hardcover | April 24, 2007

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Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,"thebranchof mathematical logic which deals with the relation between a formal language and its interpretations". No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero-one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
Erich Graedel is a Professor of Mathematical Foundations of Computer Science at the University of Technology Aachen.  His research interests include algorithms, complexity, and logic in computer science.Phokion G. Kolaitis is a professor of computer science at the University of California, Santa Cruz. His current research interests inc...
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Title:Finite Model Theory and Its ApplicationsFormat:HardcoverDimensions:440 pagesPublished:April 24, 2007Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540004289

ISBN - 13:9783540004288

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Table of 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.

Editorial Reviews

From the reviews:"This book has its origins in a workshop held in Philadelphia in 1999 . . The chapters are of an expository nature, each one providing an excellent starting point to explore the research literature in the relevant topic. . I found it to be a more accessible introduction to the subject . and a useful starting point for graduate students entering the subject. . This will appeal . to those readers trained in classical traditions of logic who wish to approach the subject." (Anuj Dawar, Mathematical Reviews, Issue 2009 i)