Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Reversible DAC and other improvements for solving Max-CSP
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Maintaining reversible DAC for Max-CSP
Artificial Intelligence
Uncertainty in Constraint Satisfaction Problems: a Probalistic Approach
ECSQARU '93 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Directed Arc Consistency Preprocessing
Constraint Processing, Selected Papers
Constraint solving over semirings
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Metric SCSPs: Partial Constraint Satisfaction via Semiring CSPs Augmented with Metrics
AI '02 Proceedings of the 15th Australian Joint Conference on Artificial Intelligence: Advances in Artificial Intelligence
Generalized Arc Consistency with Application to MaxCSP
AI '02 Proceedings of the 15th Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence
A General Scheme for Multiple Lower Bound Computation in Constraint Optimization
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Lower Bounds for Non-binary Constraint Optimization Problems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Opportunistic Specialization in Russian Doll Search
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Specific Filtering Algorithms for Over-Constrained Problems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Node and arc consistency in weighted CSP
Eighteenth national conference on Artificial intelligence
Semiring-Based Soft Constraints
Concurrency, Graphs and Models
Speeding up weighted constraint satisfaction using redundant modeling
AI'06 Proceedings of the 19th Australian joint conference on Artificial Intelligence: advances in Artificial Intelligence
Computational protein design as a cost function network optimization problem
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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Traditionally, local consistency is defined as a relaxation of consistency which can be checked in polynomial time. It is accompanied by a corresponding "filtering" or "enforcing" algorithm that computes in polynomial time, and from any given CSP, an equivalent unique CSP which satisfies the local consistency property. The question whether the notion of local consistency can be extended to soft constraint frameworks has been addressed by several papers, in several settings [4, 14, 12]. The main positive conclusion of these works is that the notion of local consistency can be extended to soft constraints frameworks which rely on an idempotent violation combination operator. However, the question whether this can be done for non idempotent operators as eg, in the Max-CSP problem, is not clear and has lead to several different notions of arc consistency [14, 16, 1, 11, 10]. Each of these proposals lacks several of the original properties of local consistency. In this paper, we show that using a small additional axiom, satisfied by most existing soft constraints proposals (including Max-CSP), it is possible to define a notion of arc consistency that keeps all the good properties of classical arc consistency but the unicity of the arc consistent closure. We show that this notion directly provides improved lower bounds. Stronger alternative definitions, that allow partial inconsistencies to propagate are also considered.