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This book is the first comprehensive survey of the field of constraint databases. Constraint databases are a fairly new and active area of database research. The key idea is that constraints, such as linear or polynomial equations, are used to represent large, or even infinite, sets in a compact way. The ability to deal with infinite sets makes constraint databases particularly promising as a technology for integrating spatial and temporal data with standard re­ lational 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 book is a collaborative effort involving many authors who have con­ tributed chapters on their fields of expertise. Despite this, the book is designed to be read as a whole, as opposed to a collection of individual surveys. In par­ ticular, the terminology and the style of presentation have been standardized, and there are multiple cross-references between the chapters. The idea of constraint databases goes back to the late Paris Kanellakis.

This Festschrift volume, published in honour of Peter Buneman, contains contributions written by some of his colleagues, former students, and friends. In celebration of his distinguished career a colloquium was held in Edinburgh, Scotland, 27-29 October, 2013. The articles presented herein belong to some of the many areas of Peter's research interests.

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.

Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target. Such a target instance should correctly represent information from the source instance under the constraints imposed by the target schema, and it should allow one to evaluate queries on the target instance in a way that is semantically consistent with the source data. Data exchange is an old problem that re-emerged as an active research topic recently, due to the increased need for exchange of data in various formats, often in e-business applications. In this lecture, we give an overview of the basic concepts of data exchange in both relational and XML contexts. We give examples of data exchange problems, and we introduce the main tasks that need to addressed. We then discuss relational data exchange, concentrating on issues such as relational schema mappings, materializing target instances (including canonical solutions and cores), query answering, and query rewriting. After that, we discuss metadata management, i.e., handling schema mappings themselves. We pay particular attention to operations on schema mappings, such as composition and inverse. Finally, we describe both data exchange and metadata management in the context of XML. We use mappings based on transforming tree patterns, and we show that they lead to a host of new problems that did not arise in the relational case, but they need to be addressed for XML. These include consistency issues for mappings and schemas, as well as imposing tighter restrictions on mappings and queries to achieve tractable query answering in data exchange. Table of Contents: Overview / Relational Mappings and Data Exchange / Metadata Management / XML Mappings and Data Exchange

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.

This volume collects the papers presented at the 10th International Conference on Database Theory, ICDT 2005, held during January 5–7, 2005, in Edinburgh, UK. ICDT (http://alpha.luc.ac.be/~lucp1080/icdt/) has now a long tra- tion of international conferences, providing a biennial scienti?c forum for the communication of high-quality and innovative research results on theoretical - pects of all forms of database systems and database technology. The conference usually takes place in Europe, and has been held in Rome (1986), Bruges (1988), Paris (1990), Berlin (1992), Prague (1995), Delphi (1997), Jerusalem (1999), London (2001), and Siena (2003) so far. ICDT has merged with the Sym- sium on Mathematical Fundamentals of Database Systems (MFDBS), initiated in Dresden in 1987, and continued in Visegrad in 1989 and Rostock in 1991. ICDT had a two-stage submission process. First, 103 abstracts were subm- ted, which were followed a week later by 84 paper submissions. From these 84 submissions, the ICDT Program Committee selected 24 papers for presentation at the conference. Most of these papers were “extended abstracts” and preli- nary reports on work in progress. It is anticipated that most of these papers will appear in a more polished form in scienti?c journals.