Constraint logic programming (CLP) is a multidisciplinary research area which can be located between Artificial Intelligence, Operation Research, and Programming Languages, and has to do with modeling, solving, and programming real-life problems which can be described as a set of statements (the constraints) which describe some relationship between the problem's variables. This survey paper gives a brief introduction to C(L)P, presents a (necessarily partial) state of the art in CLP research and applications, points out some promising directions for future applications, and discusses how to cope with current research challenges.

Constraint (logic) programming : A survey on research and applications

The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas, eg deductive databases, theorem proving, static analysis, rapid software prototyping The various solutions proposed are spread across a large literature In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory We address the problem of deciding existence of solutions at an abstract level This provides also the ability to classify different types of set unification problems Unification algorithms are uniformly proposed to solve the unification problem in each of such classes The algorithms presented are partly drawn from the literature – and properly revisited and analyzed – and partly novel proposals In particular, we present a new goal-driven algorithm for general $ACI1$ unification and a new simpler algorithm for general $(Ab)(C\ell)$ unification

Set Unification

The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas, e.g. deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes. The algorithms presented are partly drawn from the literature – and properly revisited and analyzed – and partly novel proposals. In particular, we present a new goal-driven algorithm for general $ACI1$ unification and a new simpler algorithm for general $(Ab)(C\ell)$ unification.

Set unification

In this paper we propose a semantically well-founded combination of the constraint solvers used in the constraint programming languages CLP(SET) and CLP(FD). This work demonstrates that it is possible to provide efficient executions (through CLP(FD) solvers) while maintaining the expressive power and flexibility of the CLP(SET) language. We develop a combined constraint solver and we show how static analysis can help in organizing the distribution of constraints to the two constraint solvers.

Integrating finite domain constraints and CLP with sets

The authors investigate the relationship between set constraints and the monadic class of first-order formulas and show that set constraints are essentially equivalent to the monadic class. From this equivalence, they infer that the satisfiability problem for set constraints is complete for NEXPTIME. More precisely, it is proved that this problem has a lower bound of NTIME(c/sup n/log n/), for some c>0. The relationship between set constraints and the monadic class also gives decidability and complexity results for certain practically useful extensions of set constraints, in particular "negative" projections and subterm equality tests. >

Set Constraints are the Monadic Class

Extensional Set (XS) library is an extension of ECLiPSe which solves set-theoretical constraints over extensional sets containing variables with numeric domains. To efficiently process such a class of set domains, XS library employs a constraint programming method called Subdefinite Computations. Within that framework, a domain representation and an approximate unification algorithm are proposed. The abilities of the library are illustrated by a geometric application.

Extensional Set Library for ECLiPSe

In the present paper we describe the notion of subdefinite computation models (SD-models), introduced by A.S.Narinyani to represent subdefinite information in databases of AI systems. As the algorithm for problem solving, we use the technique of constraint propagation, which significantly reduces the solution space. Application of SD-models to the routing problem is described.

FISSURE: FInder of Solutions with SUbdefinite REsources

Constraints are natural and convenient way of describing various types of relations between parameters. It's generally accepted that constraint systems can benefit to DB-systems. First they could be used for query optimization (by reducing the number of objects to be tested) both in traditional DB-systems and in databases with modern features like spatial or constraint indexes. In the former case the combination seems to be most reasonable since DB provides efficient way of handling and storing constraints which perfectly could be solved by ID-Library.

Interval Domain Library for ECLiPSe and Its Application

Origins of the subdefinite approach lie aside from constraint programming, however, the approach essentially is a consistency technique which works with abstract domains and procedurally given semantics of constraints. The approach generalizes many constraint programming techniques. We present LogiCalc, a system which uses subdefinite models for solving arbitrary equations over atoms, integers, tuples, and extensional and intentional sets. We describe its input language and some details of set processing.

Tatyana M. Yakhno

Papers

Extensional Set Library for ECLiPSe

FISSURE: FInder of Solutions with SUbdefinite REsources

Interval Domain Library for ECLiPSe and Its Application

Application of Subdefinite Models for Solving Constraint Satisfaction Problems