biblio.bib

@TECHREPORT{DFJLOT-RREMN-02,
  KEY = {DFJLOT 02},
  AUTHOR = {Romuald Debruyne and G{\'e}rard Ferrand and Narendra Jussien and Willy Lesaint and Samir Ouis and Alexandre Tessier},
  TITLE = {Correctness of Constraint Retraction Algorithms},
  INSTITUTION = {{\'E}cole des Mines de Nantes},
  YEAR = {2002},
  NUMBER = {02-6-INFO},
  ABSTRACT = {Using a filtering technique is crucial to reduce the search space. Most of the solvers (CHIP, GNU-Prolog, ILOG Solver,
CHOCO) use reduction operators and a propagation mechanism to enforce a local consistency. This scheme is quite universally used on 
static CSPs. But we do not have such an unanimity when relaxing constraints. Several techniques have been proposed to deal with 
dynamicity. The problem we address here is two-fold. First, we highlight that it is possible to generalize the proposed techniques to 
relax constraints. Second, we show a sufficient work to do in order to incrementally relax a constraint.},
  ADDRESS = {Nantes, France},
  TYPE = {Research Report},
  PDF = {http://www.emn.fr/jussien/publications/debruyne-RR0206.pdf}
}
@TECHREPORT{DFJLOT-RR2002-09,
  KEY = {DFJLOTrr 02},
  AUTHOR = {Romuald Debruyne and G{\'e}rard Ferrand and Narendra Jussien and Willy Lesaint and Samir Ouis and Alexandre Tessier},
  TITLE = {Correctness of Constraint Retraction Algorithms},
  INSTITUTION = {LIFO, University of Orl{\'e}ans},
  YEAR = {2002},
  NUMBER = {2002-09},
  ABSTRACT = {Using a filtering technique is crucial to reduce the search space. Most of the solvers (CHIP, GNU-Prolog, ILOG Solver, 
CHOCO) use reduction operators and a propagation mechanism to enforce a local consistency. This scheme is quite universally used on 
static CSPs. But we do not have such an unanimity when relaxing constraints. Several techniques have been proposed to deal with 
dynamicity. The problem we address here is two-fold. First, we highlight that it is possible to generalize the proposed techniques to 
relax constraints. Second, we show a sufficient work to do in order to incrementally relax a constraint.},
  ADDRESS = {BP 6759, F-45067 Orl{\'e}ans Cedex 2},
  MONTH = {May},
  TYPE = {Research Report},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/RR2002-09.ps.gz}
}
@TECHREPORT{FerLesTes-RR2001-05,
  KEY = {FLTrr 01},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Theoretical Foundations of Value Withdrawal Explanations in Constraints Solving by Domain Reduction},
  INSTITUTION = {LIFO, University of Orl{\'e}ans},
  YEAR = {2001},
  NUMBER = {2001-05},
  ABSTRACT = {Constraint programming is an important programming paradigm of the last years. It combines declarativity and
efficiency thanks to constraint solvers which are implemented for specific domains. We are interested here in the case of reduction of 
finite domains. In the paper, it is formalized with chaotic iterations of monotonic operators. A first notion of explanation, which have 
been proved very useful in many applications, is then defined in a declarative way in terms of closure. An explanation set for a value 
removal is a set of operators which always remove this value whatever the order of application of these operators is. A monotonic 
operator can always be defined by a set of rules (in the sense of inductive definition of Aczel). Furthermore, the paper shows that for 
classical notions of local consistency, such a system of rules can be expressed in a natural way. They express value removals as 
consequences of other value removals. So, a more precise notion of explanation can be obtained: the linking of these rules allows to 
inductively define proof trees. Such a proof tree clearly explains the removal of a value (the root of the tree) by the solver, it is 
then called an explanation for this value withdrawal. Explanations are the essence of domain reduction.},
  ADDRESS = {BP 6759, F-45067 Orl{\'e}ans Cedex 2},
  MONTH = {November},
  TYPE = {Research Report},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/RR2001-05.ps.gz}
}
@TECHREPORT{FerLesTes-RR2000-09,
  KEY = {FLTrr 00},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Value Withdrawal Explanation in {CSP}},
  INSTITUTION = {LIFO, University of Orl{\'e}ans},
  YEAR = {2000},
  NUMBER = {2000-09},
  ABSTRACT = {This work is devoted to constraint solving motivated by the debugging of constraint logic programs a la GNU-Prolog.
The paper focuses only on the constraints. In this framework, constraint solving amounts to domain reduction. A computation is
formalized by a chaotic iteration. The computed result is described as a closure. This model is well suited to the design of debugging 
notions and tools, for example failure explanations or error diagnosis. In this paper we detail an application of the model to an 
explanation of a value withdrawal in a domain. Some other works have already shown the interest of such a notion of explanation not only 
for failure analysis.},
  ADDRESS = {BP 6759, F-45067 Orl{\'e}ans Cedex 2},
  MONTH = {May},
  TYPE = {Research Report},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/RR2000-09.ps.gz}
}
@TECHREPORT{Lesaint-dea-99,
  KEY = {Les 99},
  AUTHOR = {Willy Lesaint},
  TITLE = {Simplification de Contraintes sur les Domaines Finis},
  INSTITUTION = {LIFO, University of Orl{\'e}ans},
  YEAR = {1999},
  ADDRESS = {BP 6759, F-45067 Orl{\'e}ans Cedex 2},
  MONTH = {Septembre},
  TYPE = {M{\'e}moire de DEA}
}
@UNPUBLISHED{FerLesTes-oadimpac-03,
  KEY = {FLTo 03},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Explanations and Error Diagnosis},
  YEAR = {2003},
  MONTH = {March},
  ABSTRACT = {The report proposes a theoretical approach of the debugging of constraint programs based on the notion of explanation
tree (D1.1.1 and D1.1.2 part 2). The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this 
theoretical framework for domain reduction, explanations are proof trees explaining value removals. These proof trees are defined by 
inductive definitions which express the removals of values as consequence of other value removals. Explanations may be considered as the 
essence of constraint programming. They are a declarative view of the computation trace. The diagnosis consists in locating an error in 
an explanation rooted by a symptom.},
  TYPE = {R{\'e}alisation OADymPPaC},
  NOTE = {Outils pour l'Analyse Dynamique et la mise au Point de Programmes avec Contraintes (r{\'e}alisation d3.2.2)},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/d3-2-2.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/d3-2-2.ps.gz}
}
@UNPUBLISHED{FerLesTes-oadimpac-02,
  KEY = {FLTo 02},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Un Mod{\`e}le Complet pour la Propagation et le Labeling},
  YEAR = {2002},
  MONTH = {February},
  ABSTRACT = {Ce rapport a pour but de fournir un modèle théorique pour la propagation et le labeling. Ce modèle 
est adapté aux solveurs sur domaines finis utilisés par chacun des partenaires du projet: GNU-Prolog (INRIA), CHIP (Cosytec) 
et Choco (EMN). Un calcul est formalisé par un arbre dans lequel chaque branche correspondà une itération chaotique 
d'opérateurs et où chaque feuille peut-être décrite en terme de clôture. Ce modèle est bien 
adapté aux notions d'explications qui seront utiles pour la mise au point de programmes avec contraintes. Ce rapport fait suite 
à la réalisation d1.1.1 qui traitait de la réduction de domaine. Il sera étendu pour inclure un langage 
hôte dans la prochaine réalisation.},
  TYPE = {R{\'e}alisation OADymPPaC},
  NOTE = {Outils pour l'Analyse Dynamique et la mise au Point de Programmes avec Contraintes (r{\'e}alisation d1.1.2-part2)},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/d1-1-2.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/d1-1-2.ps.gz}
}
@UNPUBLISHED{FerLesTes-oadimpac-01,
  KEY = {FLTo 01},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {A Model of Constraint Solvers by Chaotic Iteration Adapted to Value Withdrawal Explanations},
  YEAR = {2001},
  MONTH = {July},
  ABSTRACT = {The aim of this report is to provide the theoretical foundations of domain reduction. The model is well suited to the 
solvers on finite domains which are used on the respective platforms of each partner of the project: GNU-Prolog (INRIA), CHIP (COSYTEC) 
and PaLM (EMN). A computation is formalized by a chaotic iteration of operators and the result is described as a closure. The model is 
well suited to the definition of traces and explanations which will be useful for the debugging of constraint programs. This report only 
deals with the reduction stage. It will be extended to the labeling and the host language in next reports.},
  TYPE = {R{\'e}alisation OADymPPaC},
  NOTE = {Outils pour l'Analyse Dynamique et la mise au Point de Programmes avec Contraintes (r{\'e}alisation d1.1.1)},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/d1-1-1.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/d1-1-1.ps.gz}
}
@UNPUBLISHED{Trace-oadimpac-04u,
  KEY = {gentra 04},
  AUTHOR = {The {OADymPPaC} Consortium},
  TITLE = {Generic Trace Format for Constraint Programming},
  MONTH = {July},
  YEAR = {2004},
  TYPE = {R{\'e}alisation OADymPPaC},
  NOTE = {Outils pour l'Analyse Dynamique et la mise au Point de Programmes avec Contraintes (r{\'e}alisation d1.1.1)},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/gentra4cp2.1.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/gentra4cp2.1.ps.gz},
  DTD = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/gentra4cp2.1.dtd}
}
@PHDTHESIS{Lesaint-phd-03,
  KEY = {Les 03},
  AUTHOR = {Willy Lesaint},
  TITLE = {Explications de Retraits de Valeurs en Programmation par Contraintes et Application au Diagnostic D{\'e}claratif},
  SCHOOL = {Universit{\'e} d'Orl{\'e}ans},
  YEAR = {2003},
  MONTH = {Novembre},
  ABSTRACT = {Depuis quelques ann{\'e}es, la programmation par contraintes a montr{\'e} son efficacit{\'e} pour traiter les probl{\`e}mes 
difficiles, tant au point de vue de leur mod{\'e}lisation que de leur r{\'e}solution. Quand les domaines sont finis, les probl{\`e}mes ainsi 
mod{\'e}lis{\'e}s sont appel{\'e}s probl{\`e}mes de satisfaction de contraintes. Les solveurs utilis{\'e}s pour obtenir leurs solutions m{\^e}lent des 
techniques de retraits de valeurs par des notions de consistance (la r{\'e}duction de domaine) {\`a} des techniques de recherche syst{\'e}matique 
(l'{\'e}num{\'e}ration). R{\'e}cemment diff{\'e}rentes notions d'explications ont {\'e}t{\'e} introduites, que ce soit pour am{\'e}liorer l'efficacit{\'e} des m{\'e}thodes 
de l'{\'e}num{\'e}ration ou pour traiter les probl{\`e}mes sur-contraints ou dynamiques. L'id{\'e}e est d'enregistrer de l'information expliquant les 
retraits de valeurs afin de pouvoir l'utiliser, pour {\'e}viter d'explorer tout l'arbre de recherche lors de l'{\'e}num{\'e}ration, pour choisir 
une contrainte {\`a} relaxer quand un probl{\`e}me est sur-contraint ou encore pour r{\'e}introduire des valeurs dans les domaines quand une 
contrainte est relax{\'e}e. Cette th{\`e}se propose trois contributions au domaine de la programmation par contraintes. Tout d'abord la 
r{\'e}duction de domaine est formalis{\'e}e en terme ensembliste et vue comme un calcul de point fixe. Ce cadre g{\'e}n{\'e}ral, dans lequel 
l'{\'e}num{\'e}ration s'int{\`e}gre ais{\'e}ment, s'applique {\`a} tout type de solveur effectuant de la r{\'e}duction de domaine. De plus, il permet une 
d{\'e}finition naturelle d'une notion g{\'e}n{\'e}rale d'explication: les arbres explicatifs. Ces arbres de preuve sont inductivement d{\'e}finis par 
des r{\`e}gles exprimant le retrait d'une valeur comme cons{\'e}quence d'autres retraits. Les notions existantes d'explications peuvent 
ais{\'e}ment en {\^e}tre extraites. Enfin, la structure arborescente des arbres explicatif est utilis{\'e}e pour adapter le diagnostic d{\'e}claratif 
de r{\'e}ponse manquante {\`a} la programmation par contrainte. En effet, les arbres explicatifs peuvent {\^e}tre consid{\'e}r{\'e}s comme une trace 
d{\'e}clarative du calcul du solveur et peuvent donc aider {\`a} la compr{\'e}hension de l'absence d'une r{\'e}ponse.},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/these.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/these.ps.gz}
}
@INPROCEEDINGS{FerLesTes-wlpe-04,
  KEY = {FLT 04},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Explanations to Understand the Trace of a Finite Domain Constraint Solver},
  BOOKTITLE = {14th Workshop on Logic Programming Environments},
  EDITOR = {Susana Mu{\~n}oz-Hern{\'a}ndez and Jos{\'e} Manuel G{\'o}mez-P{\'e}rez and Petra Hofstedt},
  PAGES = {19--33},
  YEAR = {2004},
  ABSTRACT = {Some works in progress on finite domain constraint solvers concern the implementation of a XML trace of the 
computation according to the OADymPPaC DTD (for example in GNU-Prolog, PaLM, CHIP). Because of the large size of traces, even for small 
toy problems, some tools are needed to understand this trace. Explanations of value withdrawal (or nogoods) during domain reduction are 
used by some solvers in finite domain constraint programming. In this paper, we use a formalization of explanations by proof trees in a 
fixpoint framework based on iteration of monotonic local consistency operators. Proof trees provide a declarative view of the 
computations by constraint propagation. We show how explanations may be naturally extracted from the OADymPPaC trace format. 
Explanations allow a better understanding of the domain reductions in the trace.},
  MONTH = {September},
  ADDRESS = {Saint-Malo, France},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/wlpe2004.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/wlpe2004.ps.gz}
}
@INPROCEEDINGS{FerLesTes-aadebug-03,
  KEY = {FLT 03},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Towards Declarative Diagnosis of Constraint Programs over Finite Domains},
  BOOKTITLE = {Proceedings of the Fifth International Workshop on Automated Debugging, AADEBUG2003},
  EDITOR = {Michiel Ronsse},
  PAGES = {159--170},
  YEAR = {2003},
  ABSTRACT = {The paper proposes a theoretical approach of the debugging of constraint programs based on a notion of explanation 
tree. The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this theoretical framework for 
domain reduction, explanations are proof trees explaining value removals. These proof trees are defined by inductive definitions which 
express the removals of values as consequences of other value removals. Explanations may be considered as the essence of constraint 
programming. They are a declarative view of the computation trace. The diagnosis consists in locating an error in an explanation 
rooted by a symptom.},
  MONTH = {September},
  ADDRESS = {Ghent, Belgium},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/aadebug2003.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/aadebug2003.ps.gz}
}
@INPROCEEDINGS{Lesaint-wlpe-02,
  KEY = {Les 02},
  AUTHOR = {Willy Lesaint},
  TITLE = {Value Withdrawal Explanations: a Theoretical Tool for Programming Environments},
  BOOKTITLE = {12th Workshop on Logic Programming Environments},
  EDITOR = {Alexandre Tessier},
  PAGES = {17--33},
  YEAR = {2002},
  ABSTRACT = {Constraint logic programming combines declarativity and efficiency thanks to constraint solvers implemented for 
specific domains. Value withdrawal explanations have been efficiently used in several constraints programming environments but there 
does not exist any formalization of them. This paper is an attempt to fill this lack. Furthermore, we hope that this theoretical tool 
could help to validate some programming environments. A value withdrawal explanation is a tree describing the withdrawal of a value 
during a domain reduction by local consistency notions and labeling. Domain reduction is formalized by a search tree using two kinds 
of operators: for local consistency notions and for labeling. These operators are defined by sets of rules. Proof trees are built with 
respect to these rules. For each removed value, there exists such a proof tree which is the withdrawal explanation of this value.},
  MONTH = {July},
  ADDRESS = {Copenhagen, Denmark},
  OPTNOTE = {http://xxx.lanl.gov/html/cs/0207052},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/wlpe2002.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/wlpe2002.ps.gz}
}
@INPROCEEDINGS{FerLesTes-wflp-02,
  KEY = {FLTw 02},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Theoretical Foundations of Value Withdrawal Explanations for Domain Reduction},
  BOOKTITLE = {11th International Workshop on Functional and (Constraint) Logic Programming},
  EDITOR = {Moreno Falashi},
  PAGES = {211--224},
  YEAR = {2002},
  ABSTRACT = {Solvers on finite domains use local consistency notions to remove values from the domains. This paper defines value 
withdrawal explanations. Domain reduction is formalized with chaotic iterations of monotonic operators. To each operator is associated 
its dual which will be described by a set of rules. For classical consistency notions, there exists a natural such system of rules.
They express value removals as consequences of other value removals. The linking of these rules inductively defines proof trees. Such a 
proof tree clearly explains the removal of a value (the root of the tree). Explanations can be considered as the essence of domain 
reduction.},
  MONTH = {June},
  ADDRESS = {Grado, Italy},
  OPTNOTE = {Research Report UDMI/18/2002/RR, Universit{\`a} degli Studi di Udine},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/wflp2002.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/wflp2002.ps.gz}
}
@INPROCEEDINGS{FerLesTes-aadebug-00,
  KEY = {FLTw 00},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Value Withdrawal Explanation in {CSP}},
  BOOKTITLE = {Proceedings of the Fourth International Workshop on Automated Debugging},
  EDITOR = {Mireille Ducass{\'e}},
  YEAR = {2000},
  ABSTRACT = {This work is devoted to constraint solving motivated by the debugging of constraint logic programs a la GNU-Prolog.
The paper focuses only on the constraints. In this framework, constraint solving amounts to domain reduction. A computation is 
formalized by a chaotic iteration. The computed result is described as a closure. This model is well suited to the design of debugging 
notions and tools, for example failure explanations or error diagnosis. In this paper we detail an application of the model to an 
explanation of a value withdrawal in a domain. Some other works have already shown the interest of such a notion of explanation not 
only for failure analysis.},
  MONTH = {August},
  ADDRESS = {Munich, Germany},
  OPTNOTE = {http://xxx.lanl.gov/html/cs/0010035},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/aadebug2000.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/aadebug2000.ps.gz}
}
@INPROCEEDINGS{DFJLOT-flairs-03,
  KEY = {DFJLOT 03},
  AUTHOR = {Romuald Debruyne and G{\'e}rard Ferrand and Narendra Jussien and Willy Lesaint and Samir Ouis and Alexandre Tessier},
  TITLE = {Correctness of Constraint Retraction Algorithms},
  BOOKTITLE = {{FLAIRS'03}: Sixteenth international Florida Artificial Intelligence Research Society conference},
  PUBLISHER = {AAAI Press},
  EDITOR = {Ingrid Russell and Susan Haller},
  PAGES = {172--176},
  YEAR = {2003},
  ABSTRACT = {In this paper, we present a general scheme for incremental constraint retraction algorithms that encompasses 
all existing algorithms. Moreover, we introduce some necessary conditions to ensure the correctness of any incremental constraint 
retraction algorithms. This rather theoretical work is based on the notion of explanation for constraint programming and is 
exemplified within the PALM system: a constraint solver allowing dynamic constraint retractions.},
  MONTH = {May},
  ADDRESS = {St Augustin, Florida, USA},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/flairs2003.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/flairs2003.ps.gz}
}
@INPROCEEDINGS{FerLesTes-jfplc-04,
  KEY = {FLTj 04},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Explications pour Comprendre la Trace d'un Solveur de Contraintes sur Domaines Finis},
  YEAR = {2004},
  BOOKTITLE = {Treizi{\`e}mes Journ{\'e}es Francophones de Programmation en Logique et de programmation par Contraintes},
  PUBLISHER = {HERMES},
  EDITOR = {Fr{\'e}d{\'e}ric Mesnard},
  PAGES = {37--53},
  ABSTRACT = {Certains travaux en cours sur les solveurs de contraintes dans les domaines finis concernent l'implantation 
d'une trace XML du calcul, selon la DTD OADymPPaC (par exemple en GNU-Prolog, PaLM, CHIP). A cause de la grande taille des traces, 
m{\^e}me pour de petits exemples jouets, on a besoin d'outils pour comprendre cette trace. Des explications de retrait de valeurs (ou 
nogoods) pendant la r{\'e}duction de domaine sont utilis{\'e}es par certains solveurs en programmation par contraintes dans l es domaines 
finis. Dans ce papier, nous utilisons une formalisation des explications par des arbres de preuve dans un cadre point fixe bas{\'e} sur 
l'it{\'e}ration d'op{\'e}rateurs monotones de consistance locale. Les arbres de preuve donnent une vue d{\'e}clarative des calculs par 
propagation de contrainte. Nous montrons comment des explications peuvent {\^e}tre extraites de fa\c{c}on naturelle du format de trace 
OADymPPaC. Les explications permettent une meilleure compr{\'e}hension des r{\'e}ductions de domaine dans la trace.},
  MONTH = {June},
  ADDRESS = {Angers, France},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/jfplc2004.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/jfplc2004.ps.gz}
}
@INPROCEEDINGS{FerLesTes-exact-05,
  KEY = {FLTe 05},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Explanations and Proof Trees},
  YEAR = {2005},
  BOOKTITLE = {International Symposium on Explanation-Aware Computing, ExaCt 2005},
  PUBLISHER = {AAAI Press},
  EDITOR = {Thomas R. Roth-Berghofer and Stefan Schultz and Andrea Woody},
  PAGES = {76--85},
  ABSTRACT = {This paper proposes a model for explanations in a set theoretical framework using the notions of closure or fixpoint.
In this approach, sets of rules associated with monotonic operators allow to define proof trees. The proof trees may be considered as a 
declarative view of the trace of a computation. We claim they are explanations of the result of a computation. First, the general 
scheme is given. Then, it is applied to Constraint Logic Programming, next to Constraint Satisfaction Problems.},
  MONTH = {November},
  ADDRESS = {Washington, D.C., USA},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/exact2005.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/exact2005.ps.gz}
}
@ARTICLE{FerLesTes-cai-06,
  KEY = {FLT 06},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Explanations and Proof Trees},
  JOURNAL = {Computing and Informatics},
  VOLUME = {25},
  NUMBER = {2-3},
  YEAR = {2006},
  PAGES = {1001--1021},
  ABSTRACT = {This paper proposes a model for explanations in a set theoretical framework using the notions of closure or fixpoint.
In this approach, sets of rules associated with monotonic operators allow to define proof trees.
The proof trees may be considered as a declarative view of the trace of a computation.
We claim they are explanations of the results of a computation.
This notion of explanation is applied to constraint logic programming, and it is used for declarative error diagnosis.
It is also applied to constraint programming, and it is used for constraint retraction.},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/cai2006.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/cai2006.ps.gz}
}
@ARTICLE{FerLesTes-entcs-02,
  KEY = {FLT 02},
  AUTHOR = {G{\'e}rard Ferrand and Willy Lesaint and Alexandre Tessier},
  TITLE = {Theoretical Foundations of Value Withdrawal Explanations for Domain Reduction},
  JOURNAL = {Electronic Notes in Theoretical Computer Science},
  VOLUME = {76},
  PUBLISHER = {Elsevier},
  YEAR = {2002},
  MONTH = {November},
  ABSTRACT = {Solvers on finite domains use local consistency notions to remove values from the domains. This paper defines value 
withdrawal explanations. Domain reduction is formalized with chaotic iterations of monotonic operators. To each operator is associated 
its dual which will be described by a set of rules. For classical consistency notions, there exists a natural such system of rules.
They express value removals as consequences of other value removals. The linking of these rules inductively defines proof trees. Such 
a proof tree clearly explains the removal of a value (the root of the tree). Explanations can be considered as the essence of domain 
reduction.},
  OPTNOTE = {http://www.elsevier.com/gej-ng/31/29/23/126/23/26/76008.pdf},
  PDF = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/entcs2002.pdf},
  PS = {http://www.univ-orleans.fr/lifo/Members/lesaint/publis/entcs2002.ps.gz}
}

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