Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.

A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.

Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples,

Local consistency techniques have been introduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over nite integer domains. This makes difficult a natural and concise modelling as well as an efficient solving of a class of NP-complete combinatorial search problems dealing with sets. To overcome these problems, we propose a solution which consists in extending the notion of integer domains to that of set domains (sets of sets). We specify a set domain by an interval whose lower and upper bounds are known sets, ordered by set inclusion. We define the formal and practical framework of a new constraint logic programming language over set domains, called Conjunto. Conjunto comprises the usual set operation symbols ([ � \ � n), and the set inclusion relation (). Set expressions built using the operation symbols are interpreted as relations (s [ s1 = s2,...). In addition, Conjunto provides us with a set of constraints called graduated constraints (e.g. the set cardinality) which map sets onto arithmetic terms. This allows us to handle optimization problems by applying a cost function to the quantifiable, i.e., arithmetic, terms which are associated to set terms. The constraint solving in Conjunto is based on local consistency techniques using interval reasoning which are extended to handle set constraints. The main contribution of this paper concerns the formal definition of the language and its design and implementation as a practical language.

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This paper is a retrospective account of some of the developments leading up to, and ensuing from, the analysis of the complexity of some polynomial network consistency algorithms for constraint satisfaction problems.

Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, cross-fertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a black-box approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired

In this paper we formalise CSP solving as an inference process. Based on the notion of Computational Systems we associate actions with rewriting rules and control with strategies that establish the order of application of the inferences. The main contribution of this work is to lead the way to the design of a formalism allowing to better understand constraint solving and to apply in the domain of CSP the knowledge already developed in Automated Deduction. Keywords: Constraint Satisfaction Problems, Computational Systems, Rewriting Logic. 1 Introduction In the last twenty years many work has been done on solving Constraint Satisfaction Problems, CSP. The solvers used by constraint solving systems can be seen as encapsulated in black boxes. In this work we formalise CSP solving as an inference process. We are interested in description of constraint solving using rule-based algorithms because of the explicit distinction made in this approach between deduction rules and control. We associ...

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Constraint logic programming is often described as logic programming with unification replaced by constraint solving over a computation domain. There is another, very different, CLP paradigm based on constraint satisfaction, where program-defined goals can be treated as constraints and handled using propagation. This paper proposes a generalisation of propagation, which enables it to be applied on arbitrary computation domains, revealing that the two paradigms of CLP are orthogonal, and can be freely combined. The main idea behind generalised propagation is to use whatever constraints are available over the computation domain to express restrictions on problem variables. Generalised propagation on a goal G requires that the system extracts a constraint approximating all the answers to G. The paper introduces a generic algorithm for generalised propagation called topological branch and bound which avoids enumerating all the answers to G. Generalised propagation over the Herbrand univers...