Pierre Berlandier | University of Nice Sophia Antipolis, Nice, France (original) (raw)

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Papers by Pierre Berlandier

Research paper thumbnail of Etude de mecanismes d'interpretation de contraintes et de leur integration dans un systeme a base de connaissances

Le travail propose dans cette these part du constat que les contraintes constituent un type de co... more Le travail propose dans cette these part du constat que les contraintes constituent un type de connaissance important qui intervient dans de nombreux domaines. Il est donc crucial qu'un systeme de raisonnement a base de connaissances puisse les representer aisement et les interpreter efficacement. Cependant, on constate aussi que la plupart de ces systemes developpent leurs propres formalismes et interpretes ad-hoc car l'environnement de representation et d'interpretation des connaissances (eric) qu'ils utilisent n'offrent pas d'outils adequats. Notre but est d'essayer de combler cette lacune en etablissant un schema general d'integration d'outils de manipulation de contraintes aux eric a base d'objets structures. Dans une premiere partie, nous presentons un modele de contraintes abstrait et independant du domaine. A partir de ce modele, nous developpons un ensemble d'outils pour la satisfaction de problemes et le maintien de leur coherence. Le probleme de satisfaction est etudie pour les domaines finis et le maintien de coherence utilise un mecanisme de propagation de valeurs dont l'applicabilite est generale. Dans une seconde partie, nous montrons comment un eric peut s'approprier ces outils par l'instanciation d'une representation par objets du modele des contraintes et d'une interface fonctionnelle reduite. Le resultat est un systeme souple, qui n'est pas alourdi par l'adjonction d'un formalisme supplementaire. Un exemple d'integration dans le noyau de systeme expert smeci montre quels roles peuvent servir les differents types d'interpretation des contraintes. Enfin, nous proposons deux nouvelles formes de contraintes: les contraintes de transition et les metacontraintes. Les premieres permettent d'exercer un controle constant sur l'evolution des objets de l'eric. Les secondes decoulent de la representation homogene des contraintes et des objets contraints. Elles permettent de representer des problemes dont la structure s'ajuste automatiquement en fonction de l'evolution des objets contraints

Research paper thumbnail of Une application pragmatique de la consistance de chemins

Research paper thumbnail of The use and interpretation of meta level constraints

Springer eBooks, 1993

This paper introduces a model for dynamic constraint problems in which constraints and variables ... more This paper introduces a model for dynamic constraint problems in which constraints and variables are comparable entities. This model provides a natural way to represent configuration or design problems wherein the set of objects and their constraints are bound to evolve during the solving process. Metaconstraints, i.e. constraints on constraint descriptions, are the central contribution of the model. Depending on which part of the description (the set of constrained variables or the relation that links them) they apply to, metaconstraints can be used to monitor the evolution of the problem's variables or constraints. The implications of metaconstraints on the consistency maintenance process are studied and an implementation within the Prose constraint language is briefly described.

Research paper thumbnail of Improving domain filtering using restricted path consistency

This paper introduces a new level of partial consistency for constraint satisfaction problems, wh... more This paper introduces a new level of partial consistency for constraint satisfaction problems, which is situated between arc and path-consistency. We call this level restricted path-consistency (RPC). Two procedures to enforce complete and partial RPC are presented. They both use path-based verifications to detect inconsistencies but retain the good features of arc-consistency since they only touch the variables domains and do not augment the connectivity of the constraint graph. We show that, although they perform a limited number of checks, these procedures exhibit a considerable pruning power.<<ETX>>

Research paper thumbnail of Integration d'outils pour l'expression et la satisfaction de contraintes dans un generateur de systemes experts

Integration d'outils pour l'expression et la satisfaction de contraintes dans un generateur de sy... more Integration d'outils pour l'expression et la satisfaction de contraintes dans un generateur de systemes experts. [Rapport de recherche] RR-0924, INRIA. 1988.

Research paper thumbnail of Deux variations sur le thème de la consistance d'arcs : maintien et renforcement

Research paper thumbnail of Constraint driven computations in evolving object databases

[1990] Proceedings of the 2nd International IEEE Conference on Tools for Artificial Intelligence, Dec 4, 2002

PROSE, a generic package for maintaining the consistency of object databases using constraint dri... more PROSE, a generic package for maintaining the consistency of object databases using constraint driven computations is discussed. Two original contributions of the package which arose from the meeting of objects and constraints are described. First, due to its reflective implementation, PROSE makes it possible keep consistency not only for the database entities but also for the constraint networks it builds. Second, it provides the user with temporal constraints that help supervise the evolution of the entities between arbitrary time events. A validation of this approach is shown by describing an instantiation of PROSE for an expert system shell.<<ETX>>

Research paper thumbnail of Représentation et traitement pratique de la flexibilité dans les problèmes sous contraintes

Journées Nationales PRC …, 1992

Research paper thumbnail of Maintaining arc consistency through constraint retraction

Proceedings Sixth International Conference on Tools with Artificial Intelligence. TAI 94

To cope with a growing number of applications, thebasic formalism of constraint satisfaction prob... more To cope with a growing number of applications, thebasic formalism of constraint satisfaction problems hasto be augmented in various directions. One of these directionsis the concept of dynamic constraint problemsi.e. problems to which constraints can be added but alsoretracted at any time. To handle dynamic problems, itis important to adapt efficiently the solving proceduresthat are available on static ones. Of

Research paper thumbnail of Improving domain filtering using restricted path consistency

Proceedings the 11th Conference on Artificial Intelligence for Applications

This paper introduces a new level of partial consistency for constraint satisfaction problems, wh... more This paper introduces a new level of partial consistency for constraint satisfaction problems, which is situated between arc and path-consistency. We call this level restricted path-consistency (RPC). Two procedures to enforce complete and partial RPC are presented. They both use path-based verifications to detect inconsistencies but retain the good features of arcconsistency since they only touch the variables domains and do not augment the connectivity of the constraint graph. We show that, although they perform a limited number of checks, these procedures exhibit a considerable pruning power.

Research paper thumbnail of Prose: A constraint language with control structures

Lecture Notes in Computer Science, 1989

Constraint languages tend to lack some computational capabilities that are crucial to any program... more Constraint languages tend to lack some computational capabilities that are crucial to any programming language. Those capabilities range from control structures such as conditionals or iteration to recursive constructions.

Research paper thumbnail of A Non-diffident Combinatorial Optimization Algorithm

Branch and bound is a well known, allpurpose optimization strategy. It relies on the availability... more Branch and bound is a well known, allpurpose optimization strategy. It relies on the availability of a search tree evaluation function and maintains an upper bound cost as a reference for the pruning. This upper bound is updated each time a better solution is encountered. In this paper, we propose a non-diffident optimization strategy that imposes this value. The computation of the bound is based on some heuristics that use probabilistic knowledge of the problem. Setting an arbitrary upper bound enables a faster convergence towards the best solution. The counterpart is that the search tree might be traversed more than once. However, we show in an experimental evaluation that our approach remains beneficial.

Research paper thumbnail of Autour Du Problème De Satisfaction De Contraintes

Introduction Le cadre des problemes de satisfaction de contraintes ou CSP (pour Constraint Satisf... more Introduction Le cadre des problemes de satisfaction de contraintes ou CSP (pour Constraint Satisfaction Problems) a pour finalite l'expression et la resolution de problemes faisant intervenir des contraintes. De facon tres generale, une contrainte correspond a l'enonce d'une proprie te relative a certaines caracteristiques de differents objets : propriete physique (spatiotemporelle. ..) necessairement satisfaite par les objets consideres ou propriete desiree par l'utilisateur par exemple. Du fait de sa generalite, il est assez naturel que la notion de contrainte soit frequemment utilisee et ait recu beaucoup d'attention de la part des communautes de l'intelligence artificielle ou de la recherche operationnelle, toutes deux preoccupees par la representation et la resolution de problemes. Face aux illustres predecesseurs que sont la programmation lineaire (en nombres entiers) ou la logique propositionnelle, le cad

Research paper thumbnail of A Performance Evaluation of Backtrack-Bounded Search Methods for N-ary Constraint Networks

An early study on the structural aspect of binary constraint problems has led to the definition o... more An early study on the structural aspect of binary constraint problems has led to the definition of a backtrack bounded solving (BBS) method. In this paper, we apply this method to n-ary constraint problems and we try to weigh the benefits that can be expected from its use. Simple functions are described to implement BBS for acyclic n-ary problems and results of an experimental performance evaluation are given.

Research paper thumbnail of A Symbiotic Approach to Arc and Path Consistency Checking

The resolution of constraint satisfaction problems heavily relies on the use of local consistency... more The resolution of constraint satisfaction problems heavily relies on the use of local consistency enforcement procedures which are used to filter the problems before or during their resolution. While procedures based on arc-consistency are almost a standard, path-consistency checking is often neglected because it is costly and it filters out pairs of assignments instead of single assignments. This paper presents a domain filtering procedure that tightly combines the use of arc and pathconsistency, each one helping the other to achieve further or faster work. We show, on an experimental evaluation, that the proposed procedure offers a considerable filtering power at relatively low cost.

Research paper thumbnail of Filtrage De Problemes Par Consistance De Chemin Restreinte

... résolution est tre`s ap-préciable dans certains cas. Un travail a` venir est d'explorer ... more ... résolution est tre`s ap-préciable dans certains cas. Un travail a` venir est d'explorer les bénéfices de l'utilisa-tion de P-RPC au cours de la recherche comme cela est fait avec AC dans l'algorithme MAC [SAB 94]. 5 Conclusion ...

Research paper thumbnail of The Use and Interpretation of Meta Level Constraints

This paper introduces a model for dynamic constraint problems in which constraints and variables ... more This paper introduces a model for dynamic constraint problems in which constraints and variables are comparable entities. This model provides a natural way to represent configuration or design problems wherein the set of objects and their constraints are bound to evolve during the solving process. Metaconstraints, i.e. constraints on constraint descriptions, are the central contribution of the model. Depending on which part of the description (the set of constrained variables or the relation that links them) they apply to, metaconstraints can be used to monitor the evolution of the problem's variables or constraints. The implications of metaconstraints on the consistency maintenance process are studied and an implementation within the Prose constraint language is briefly described.

Research paper thumbnail of Integration d'outils pour l'expression et la satisfaction de contraintes dans un generateur de systemes experts

Les langages a base de contraintes apparaissent comme des outils efficaces pour la modelisation, ... more Les langages a base de contraintes apparaissent comme des outils efficaces pour la modelisation, la simulation et la resolution de problemes. L'integration d'un systeme de gestion de contraintes a base de dependances dans un generateur de systemes experts renforce la puissance de chacun des deux outils. Neanmoins, les langages de contraintes classiques se revelent mal adaptes a la gestion d'environnements tels que les bases de faits des systemes experts. Nous presentons dans ce papier une representation des contraintes a caractere reflexif. Les meta-contraintes qui en resultent permettent la gesiton explicite de l'ensemble des dependances des contraintes de niveau objet. On conserve ainsi non seulement la coherence des valeurs du reseau de contraintes mais aussi la coherence du reseau lui-meme vis-a-vis de la base de faits. Cette representation implique des changements importants sur l'algorithme de propagation de contraintes classique.

Research paper thumbnail of Arc-Consistency for Dynamic Constraint Problems: An RMS-Free Approach

With the rapid development of constraint programminghas emerged the need for consistency maintena... more With the rapid development of constraint programminghas emerged the need for consistency maintenance procedures that support eeciently dynamic problems i.e. problems to which constraints can be added but also retracted. This paper presents such a procedure which, contrary to previous approaches , does not rely on any reason maintenance system and consequently has the advantage of a low space complexity. We give the detailed algorithm of the procedure and an experimental evaluation of its performances. We also highlight some beneets gained by our approach regarding exibil-ity and extensibility.

Research paper thumbnail of Deux variations sur le thème de la consistance d'arcs : maintien et renforcement

etablir un niveau de consistance partielle au sein d'un probleme de satisfaction de contraint... more etablir un niveau de consistance partielle au sein d'un probleme de satisfaction de contraintes est une etape importante, sinon necessaire, de son processus de resolution. Ce rapport presente deux variations sur le theme de la consistance d'arcs qui reste aujourd'hui le niveau de consistance le plus souvent sollicite en pratique. La premiere variation est une extension de la consistance d'arcs classique au cadre des problemes de contraintes dynamiques. Ces problemes possedent un cycle de vie du a des interactions avec l'utilisateur qui peut ajouter et retirer des contraintes a tout moment. Le probleme principal est alors de maintenir la consistance d'arcs a travers le retrait de contraintes. La seconde variation traite d'un leger renforcement de la condition qui caracterise la consistance d'arcs afin d'offrir une meilleure capacite de filtrage des domaines. Le niveau de consistance partiel obtenu se situe entre la consistance d'arcs et la cons...

Research paper thumbnail of Etude de mecanismes d'interpretation de contraintes et de leur integration dans un systeme a base de connaissances

Le travail propose dans cette these part du constat que les contraintes constituent un type de co... more Le travail propose dans cette these part du constat que les contraintes constituent un type de connaissance important qui intervient dans de nombreux domaines. Il est donc crucial qu'un systeme de raisonnement a base de connaissances puisse les representer aisement et les interpreter efficacement. Cependant, on constate aussi que la plupart de ces systemes developpent leurs propres formalismes et interpretes ad-hoc car l'environnement de representation et d'interpretation des connaissances (eric) qu'ils utilisent n'offrent pas d'outils adequats. Notre but est d'essayer de combler cette lacune en etablissant un schema general d'integration d'outils de manipulation de contraintes aux eric a base d'objets structures. Dans une premiere partie, nous presentons un modele de contraintes abstrait et independant du domaine. A partir de ce modele, nous developpons un ensemble d'outils pour la satisfaction de problemes et le maintien de leur coherence. Le probleme de satisfaction est etudie pour les domaines finis et le maintien de coherence utilise un mecanisme de propagation de valeurs dont l'applicabilite est generale. Dans une seconde partie, nous montrons comment un eric peut s'approprier ces outils par l'instanciation d'une representation par objets du modele des contraintes et d'une interface fonctionnelle reduite. Le resultat est un systeme souple, qui n'est pas alourdi par l'adjonction d'un formalisme supplementaire. Un exemple d'integration dans le noyau de systeme expert smeci montre quels roles peuvent servir les differents types d'interpretation des contraintes. Enfin, nous proposons deux nouvelles formes de contraintes: les contraintes de transition et les metacontraintes. Les premieres permettent d'exercer un controle constant sur l'evolution des objets de l'eric. Les secondes decoulent de la representation homogene des contraintes et des objets contraints. Elles permettent de representer des problemes dont la structure s'ajuste automatiquement en fonction de l'evolution des objets contraints

Research paper thumbnail of Une application pragmatique de la consistance de chemins

Research paper thumbnail of The use and interpretation of meta level constraints

Springer eBooks, 1993

This paper introduces a model for dynamic constraint problems in which constraints and variables ... more This paper introduces a model for dynamic constraint problems in which constraints and variables are comparable entities. This model provides a natural way to represent configuration or design problems wherein the set of objects and their constraints are bound to evolve during the solving process. Metaconstraints, i.e. constraints on constraint descriptions, are the central contribution of the model. Depending on which part of the description (the set of constrained variables or the relation that links them) they apply to, metaconstraints can be used to monitor the evolution of the problem's variables or constraints. The implications of metaconstraints on the consistency maintenance process are studied and an implementation within the Prose constraint language is briefly described.

Research paper thumbnail of Improving domain filtering using restricted path consistency

This paper introduces a new level of partial consistency for constraint satisfaction problems, wh... more This paper introduces a new level of partial consistency for constraint satisfaction problems, which is situated between arc and path-consistency. We call this level restricted path-consistency (RPC). Two procedures to enforce complete and partial RPC are presented. They both use path-based verifications to detect inconsistencies but retain the good features of arc-consistency since they only touch the variables domains and do not augment the connectivity of the constraint graph. We show that, although they perform a limited number of checks, these procedures exhibit a considerable pruning power.<<ETX>>

Research paper thumbnail of Integration d'outils pour l'expression et la satisfaction de contraintes dans un generateur de systemes experts

Integration d'outils pour l'expression et la satisfaction de contraintes dans un generateur de sy... more Integration d'outils pour l'expression et la satisfaction de contraintes dans un generateur de systemes experts. [Rapport de recherche] RR-0924, INRIA. 1988.

Research paper thumbnail of Deux variations sur le thème de la consistance d'arcs : maintien et renforcement

Research paper thumbnail of Constraint driven computations in evolving object databases

[1990] Proceedings of the 2nd International IEEE Conference on Tools for Artificial Intelligence, Dec 4, 2002

PROSE, a generic package for maintaining the consistency of object databases using constraint dri... more PROSE, a generic package for maintaining the consistency of object databases using constraint driven computations is discussed. Two original contributions of the package which arose from the meeting of objects and constraints are described. First, due to its reflective implementation, PROSE makes it possible keep consistency not only for the database entities but also for the constraint networks it builds. Second, it provides the user with temporal constraints that help supervise the evolution of the entities between arbitrary time events. A validation of this approach is shown by describing an instantiation of PROSE for an expert system shell.<<ETX>>

Research paper thumbnail of Représentation et traitement pratique de la flexibilité dans les problèmes sous contraintes

Journées Nationales PRC …, 1992

Research paper thumbnail of Maintaining arc consistency through constraint retraction

Proceedings Sixth International Conference on Tools with Artificial Intelligence. TAI 94

To cope with a growing number of applications, thebasic formalism of constraint satisfaction prob... more To cope with a growing number of applications, thebasic formalism of constraint satisfaction problems hasto be augmented in various directions. One of these directionsis the concept of dynamic constraint problemsi.e. problems to which constraints can be added but alsoretracted at any time. To handle dynamic problems, itis important to adapt efficiently the solving proceduresthat are available on static ones. Of

Research paper thumbnail of Improving domain filtering using restricted path consistency

Proceedings the 11th Conference on Artificial Intelligence for Applications

This paper introduces a new level of partial consistency for constraint satisfaction problems, wh... more This paper introduces a new level of partial consistency for constraint satisfaction problems, which is situated between arc and path-consistency. We call this level restricted path-consistency (RPC). Two procedures to enforce complete and partial RPC are presented. They both use path-based verifications to detect inconsistencies but retain the good features of arcconsistency since they only touch the variables domains and do not augment the connectivity of the constraint graph. We show that, although they perform a limited number of checks, these procedures exhibit a considerable pruning power.

Research paper thumbnail of Prose: A constraint language with control structures

Lecture Notes in Computer Science, 1989

Constraint languages tend to lack some computational capabilities that are crucial to any program... more Constraint languages tend to lack some computational capabilities that are crucial to any programming language. Those capabilities range from control structures such as conditionals or iteration to recursive constructions.

Research paper thumbnail of A Non-diffident Combinatorial Optimization Algorithm

Branch and bound is a well known, allpurpose optimization strategy. It relies on the availability... more Branch and bound is a well known, allpurpose optimization strategy. It relies on the availability of a search tree evaluation function and maintains an upper bound cost as a reference for the pruning. This upper bound is updated each time a better solution is encountered. In this paper, we propose a non-diffident optimization strategy that imposes this value. The computation of the bound is based on some heuristics that use probabilistic knowledge of the problem. Setting an arbitrary upper bound enables a faster convergence towards the best solution. The counterpart is that the search tree might be traversed more than once. However, we show in an experimental evaluation that our approach remains beneficial.

Research paper thumbnail of Autour Du Problème De Satisfaction De Contraintes

Introduction Le cadre des problemes de satisfaction de contraintes ou CSP (pour Constraint Satisf... more Introduction Le cadre des problemes de satisfaction de contraintes ou CSP (pour Constraint Satisfaction Problems) a pour finalite l'expression et la resolution de problemes faisant intervenir des contraintes. De facon tres generale, une contrainte correspond a l'enonce d'une proprie te relative a certaines caracteristiques de differents objets : propriete physique (spatiotemporelle. ..) necessairement satisfaite par les objets consideres ou propriete desiree par l'utilisateur par exemple. Du fait de sa generalite, il est assez naturel que la notion de contrainte soit frequemment utilisee et ait recu beaucoup d'attention de la part des communautes de l'intelligence artificielle ou de la recherche operationnelle, toutes deux preoccupees par la representation et la resolution de problemes. Face aux illustres predecesseurs que sont la programmation lineaire (en nombres entiers) ou la logique propositionnelle, le cad

Research paper thumbnail of A Performance Evaluation of Backtrack-Bounded Search Methods for N-ary Constraint Networks

An early study on the structural aspect of binary constraint problems has led to the definition o... more An early study on the structural aspect of binary constraint problems has led to the definition of a backtrack bounded solving (BBS) method. In this paper, we apply this method to n-ary constraint problems and we try to weigh the benefits that can be expected from its use. Simple functions are described to implement BBS for acyclic n-ary problems and results of an experimental performance evaluation are given.

Research paper thumbnail of A Symbiotic Approach to Arc and Path Consistency Checking

The resolution of constraint satisfaction problems heavily relies on the use of local consistency... more The resolution of constraint satisfaction problems heavily relies on the use of local consistency enforcement procedures which are used to filter the problems before or during their resolution. While procedures based on arc-consistency are almost a standard, path-consistency checking is often neglected because it is costly and it filters out pairs of assignments instead of single assignments. This paper presents a domain filtering procedure that tightly combines the use of arc and pathconsistency, each one helping the other to achieve further or faster work. We show, on an experimental evaluation, that the proposed procedure offers a considerable filtering power at relatively low cost.

Research paper thumbnail of Filtrage De Problemes Par Consistance De Chemin Restreinte

... résolution est tre`s ap-préciable dans certains cas. Un travail a` venir est d'explorer ... more ... résolution est tre`s ap-préciable dans certains cas. Un travail a` venir est d'explorer les bénéfices de l'utilisa-tion de P-RPC au cours de la recherche comme cela est fait avec AC dans l'algorithme MAC [SAB 94]. 5 Conclusion ...

Research paper thumbnail of The Use and Interpretation of Meta Level Constraints

This paper introduces a model for dynamic constraint problems in which constraints and variables ... more This paper introduces a model for dynamic constraint problems in which constraints and variables are comparable entities. This model provides a natural way to represent configuration or design problems wherein the set of objects and their constraints are bound to evolve during the solving process. Metaconstraints, i.e. constraints on constraint descriptions, are the central contribution of the model. Depending on which part of the description (the set of constrained variables or the relation that links them) they apply to, metaconstraints can be used to monitor the evolution of the problem's variables or constraints. The implications of metaconstraints on the consistency maintenance process are studied and an implementation within the Prose constraint language is briefly described.

Research paper thumbnail of Integration d'outils pour l'expression et la satisfaction de contraintes dans un generateur de systemes experts

Les langages a base de contraintes apparaissent comme des outils efficaces pour la modelisation, ... more Les langages a base de contraintes apparaissent comme des outils efficaces pour la modelisation, la simulation et la resolution de problemes. L'integration d'un systeme de gestion de contraintes a base de dependances dans un generateur de systemes experts renforce la puissance de chacun des deux outils. Neanmoins, les langages de contraintes classiques se revelent mal adaptes a la gestion d'environnements tels que les bases de faits des systemes experts. Nous presentons dans ce papier une representation des contraintes a caractere reflexif. Les meta-contraintes qui en resultent permettent la gesiton explicite de l'ensemble des dependances des contraintes de niveau objet. On conserve ainsi non seulement la coherence des valeurs du reseau de contraintes mais aussi la coherence du reseau lui-meme vis-a-vis de la base de faits. Cette representation implique des changements importants sur l'algorithme de propagation de contraintes classique.

Research paper thumbnail of Arc-Consistency for Dynamic Constraint Problems: An RMS-Free Approach

With the rapid development of constraint programminghas emerged the need for consistency maintena... more With the rapid development of constraint programminghas emerged the need for consistency maintenance procedures that support eeciently dynamic problems i.e. problems to which constraints can be added but also retracted. This paper presents such a procedure which, contrary to previous approaches , does not rely on any reason maintenance system and consequently has the advantage of a low space complexity. We give the detailed algorithm of the procedure and an experimental evaluation of its performances. We also highlight some beneets gained by our approach regarding exibil-ity and extensibility.

Research paper thumbnail of Deux variations sur le thème de la consistance d'arcs : maintien et renforcement

etablir un niveau de consistance partielle au sein d'un probleme de satisfaction de contraint... more etablir un niveau de consistance partielle au sein d'un probleme de satisfaction de contraintes est une etape importante, sinon necessaire, de son processus de resolution. Ce rapport presente deux variations sur le theme de la consistance d'arcs qui reste aujourd'hui le niveau de consistance le plus souvent sollicite en pratique. La premiere variation est une extension de la consistance d'arcs classique au cadre des problemes de contraintes dynamiques. Ces problemes possedent un cycle de vie du a des interactions avec l'utilisateur qui peut ajouter et retirer des contraintes a tout moment. Le probleme principal est alors de maintenir la consistance d'arcs a travers le retrait de contraintes. La seconde variation traite d'un leger renforcement de la condition qui caracterise la consistance d'arcs afin d'offrir une meilleure capacite de filtrage des domaines. Le niveau de consistance partiel obtenu se situe entre la consistance d'arcs et la cons...