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Reviewer: Alexei P. Stolboushkin

This book describes the syntax and semantics of a new logical programming language called LDL. Although in the standard approach to designing databases the database language (for example, SQL) is quite simple and supports only a few operations with data, such as storing and searching, the programmer ought to use some host language to manipulate the data. On the other hand, a knowledge base provides sophisticated tools to represent complex classification schemes and supports logical inference over these structures, but it is usually quite limited with respect to the total volume of data (that is, represented knowledge). LDL combines the features of logic programming languages and database languages. The book contains 10 chapters and five appendices. The first chapter, entitled “Warming Up,” is a very informal introduction. The remaining chapters describe LDL. The authors start with a very simple subset of the language, namely first-order LDL programs (chapter 2). Then they extend the language step by step by adding, in each chapter, some new language constructs. Each chapter gives the semantics of the new constructs, such as declarative semantics, which defines the meaning of programs in a nonconstructive logical sense by defining the notion of minimal model, bottom-up semantics, which defines how this minimal model is to be constructed, and top-down evaluation, which provides a constructive proof-theoretic method of assigning meaning to a formula. Chapter 3 introduces recursive rules in programs, and chapter 4 discusses interpreted predicates and functions. (Actually, the goal is to install arithmetic in the language.) Chapter 5 describes how to use negation in programs, chapter 6 introduces set terms, and chapter 7 introduces constructs to allow update operations on the facts of the database. Chapter 8 introduces some imperative constructs in the language, such as if-then-else and iteration. Chapter 9 discusses tools that define aggregate operations on sets, such as finding the minimal element. In this connection, the chapter introduces the choice predicate, which allows nondeterministic choices in programs. Chapter 10 explains how to run LDL programs in the current implementation. The appendices give the formal LDL syntax and some LDL applications and discuss some problems related to the effective implementation of LDL constructs. Throughout the book, many results related to the theoretical foundations of LDL are mentioned, but often they are neither precisely formulated nor proved. The purpose of this book is not to discuss underlying theory but to give the syntax and semantics of LDL, and this is done well. The book, which is clearly written, successfully combines formal and informal methods of presentation and contains many good examples. It really can be used to learn LDL, even by those readers who are only casually familiar with logic programming and databases. It will be interesting to specialists in these fields. The book ends with a bibliography and includes some incomplete references. For example, the result about the undecidability of the safety problem (subsection 2.4.3) was first proved in Stolboushkin et al. [1]. In relation to subsection 5.9, a good reference is Harel and Peleg [2], which gives a survey of relationships between query languages and different complexity classes.