This is the first comprehensive survey of the field of constraint databases, written by leading researchers. Constraint databases are a fairly new and active area of database research. Their ability to deal with infinite sets makes them particularly promising as a technology for integrating spatial and temporal data with standard relational databases. Constraint databases bring techniques from a variety of fields, such as logic and model theory, algebraic and computational geometry, as well as symbolic computation, to the design and analysis of data models and query languages.

This is the first comprehensive survey of the field of constraint databases, written by leading researchers. Constraint databases are a fairly new and active area of database research. Their ability to deal with infinite sets makes them particularly promising as a technology for integrating spatial and temporal data with standard relational databases. Constraint databases bring techniques from a variety of fields, such as logic and model theory, algebraic and computational geometry, as well as symbolic computation, to the design and analysis of data models and query languages.

The ?rst International Symposium on the Applications of Constraint Databases (CDB2004) took place in Paris, France, on June 12–13, 2004, just before the ACM SIGMOD and PODS conferences. Since the publication of the paper “Constraint Query Languages” by Kan- lakis, Kuper and Revesz in 1990, the last decade has seen a growing interest in constraint database theory, query evaluation, and applications, re?ected in a variety of conferences, journals, and books. Constraint databases have proven to be extremely ?exible and adoptable in environments that relational database systems cannot serve well, such as geographic information systems and bioinf- matics. This symposium brought together people from several diverse areas all c- tributing to the practice and the application of constraint databases. It was a continuation and extension of previous workshops held in Friedrichshafen, G- many (1995), Cambridge, USA (1996), Delphi, Greece (1997), and Seattle, USA (1998) as well as of the work in the comprehensive volume “Constraint Data- ses” edited by G. Kuper, L. Libkin and J. Paredaens (2000) and the textbook “Introduction to Constraint Databases” by P. Revesz (2002). The aim of the symposium was to open new and future directions in c- straint database research; to address constraints over domains other than the reals; to contribute to a better implementation of constraint database systems, in particular of query evaluation; to address e?cient quanti?er elimination; and to describe applications of constraint databases.

Differing from other books on the subject, this one uses the framework of constraint databases to provide a natural and powerful generalization of relational databases. An important theme running through the text is showing how relational databases can smoothly develop into constraint databases, without sacrificing any of the benefits of relational databases whilst gaining new advantages. Peter Revesz begins by discussing data models and how queries may be addressed to them. From here, he develops the theory of relational and constraint databases, including Datalog and the relational calculus, concluding with three sample constraint database systems -- DISCO, DINGO, and RATHER. Advanced undergraduates and graduates in computer science will find this a clear introduction to the subject, while professionals and researchers will appreciate this novel perspective on their subject.

This volume is the proceedings of the Second International Workshop on the Principles and Practice of Constraint Programming, held at Rosario, Orcas Island, Washington, USA in May 1994 in cooperation with AAAI and ALP. The volume contains 27 full revised papers selected from 87 submissions as well as a summary of a panel session on commercial applications of constraint programming. The contributions cover a broad range of topics including constraint programming languages, algorithms for constraint satisfaction and entailment, and constraints and their relation to fields such as artificial intelligence, databases, operations research, problem solving, and user interfaces.

Constraint programming aims at supporting a wide range of complex applications, which are often modeled naturally in terms of constraints. Early work, in the 1960s and 1970s, made use of constraints in computer graphics, user interfaces, and artificial intelligence. Such work introduced a declarative component in otherwise-procedural systems to reduce the development effort.

Constraints have emerged as the basis of a representational and computational paradigm that draws from many disciplines and can be brought to bear on many problem domains. This volume contains papers dealing with all aspects of c- puting with constraints. In particular, there are several papers on applications of constraints, re?ecting the practical usefulness of constraint programming. The papers were presented at the 1998 International Conference on Principles and Practice of Constraint Programming (CP’98), held in Pisa, Italy, 26{30 - tober, 1998. It is the fourth in this series of conferences, following conferences in Cassis (France), Cambridge (USA), and Schloss Hagenberg (Austria). We received 115 high quality submissions. In addition, 7 abstracts submissions were not followed by a full paper, hence were not counted as submissions. The program committee selected 29 high quality papers after thorough refereeing by at least 3 experts and further discussion by committee members. We thank the referees and the program committee for the time and e ort spent in reviewing the papers. The program committee invited three speakers: { Joxan Ja ar { Peter Jeavons { Patrick Prosser Their papers are in this volume.

This book constitutes the proceedings of the First International Conference on Principles and Practice of Constraint Programming, CP '95, held in Cassis near Marseille, France in September 1995. The 33 refereed full papers included were selected out of 108 submissions and constitute the main part of the book; in addition there is a 60-page documentation of the four invited papers and a section presenting industrial reports. Thus besides having a very strong research component, the volume will be attractive for practitioners. The papers are organized in sections on efficient constraint handling, constraint logic programming, concurrent constraint programming, computational logic, applications, and operations research.

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.