Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
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
Uncertainty in Constraint Satisfaction Problems: a Probalistic Approach
ECSQARU '93 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Encoding Partial Constraint Satisfaction in the Semiring-Based Framework for Soft Constraints
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
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The Semiring Constraint Satisfaction Problem (SCSP) framework is a popular approach for the representation of partial constraint satisfaction problems. In this framework preferences can be associated with tuples of values of the variable domains. Bistarelli et al. [S. Bistarelli, U. Montanari, F. Rossi, Semiring-based constraint solving and optimization, Journal of the ACM 44 (2) (1997) 201-236] defines a maximal solution to a SCSP as the best set of solution tuples for the variables in the problem. Sometimes this maximal solution may not be good enough, and in this case we want to change the constraints so that we solve a problem that is slightly different from the original problem but has an acceptable solution. We propose a relaxation of a SCSP, and use a semiring to give a measure of the difference between the original SCSP and the relaxed SCSP. We introduce a relaxation scheme but do not address the computational aspects.