Finite Model Theory and Its Applications

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.

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.

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 include logic in computer science, computational complexity, and database theory. He earned a Diploma in Mathematics from the University of Athens, Greece in 1973, and a Ph.D. in Mathematics from the University of California, Los Angeles in 1978. Before joining UC Santa Cruz in 1988, he served as an L.E. Dickson Instructor of Mathematics at the University of Chicago, a faculty member at Occidental College, a visiting faculty member at Stanford University, and a visiting scientist at the IBM Almaden Research Center. Kolaitis was awarded a Guggenheim Fellowship during 1993-94. In 1995, he received an Excellence in Teaching Award by the graduating computer science and computer engineering students at UC Santa Cruz.

Leonid Libkin received his PhD from the University of Pennsylvania and is currently Professor of Computer Science at the University of Toronto. His main research interests include databases and applications of logic in computer science.

Maarten Marx is an associate professor at the Vrije Universiteit Amsterdam. His research interests are in modal and algebraic logic.

Joel Spencer is a Professor of Mathematics and Computer Scienceat the Courant Institute, New York University. His research interests lie in interface between Discrete Mathematics and Theoretical Computer Science, most particularly with the Probabilistic Method as developed by Paul Erdos.

Moshe Y. Vardi is a Noah Harding Professor of Computer Science and Chair of Computer Science at Rice University. Prior to joining Rice in 1993, he was at the IBM Almaden Research Center, where he managed the Mathematics and Related Computer Science Department. His research interests include database systems, computational-complexity theory, multi-agent systems, and design specification and verification. Vardi received his Ph.D. from the Hebrew University of Jerusalem in 1981. He is the author and co-author of over 120 technical papers, as well as a book titled "Reasoning about Knowledge". Vardi is the recipient of 3 IBM Outstanding Innovation Awards. He is an editor of several international journals and is a Fellow of the Association of Computing Machinery.

Yde Venema studied mathematics; in 1992, he received a PhD in Logic with the dissertation `Many-Dimensional Modal Logic'. He is currently a Research Fellow of the Royal Netherlands Academy of Arts and Sciences and an assistant professor at the Institute for Logic, Language and Computation of the University of Amsterdam. His research interests include modal and temporal logic, algebraic logic, and applications of logic in linguistics and computer science.

Scott Weinstein is Professor of Computer Science, Mathematics, and Philosophy at the University of Pennsylvania. His research interests include logic in computer science and the philosphy of mathematics.