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Semirings for Soft Constraint Solving and Programming Jr McClellan's Military Career Reviewed andConstraint satisfaction and constraint programming have shown to be very simple but powerful ideas, with applications in various areas. Still, in the last ten years, the simple notion of constraints has shown some deficiencies concerning both theory and practice, typically in the way over constrained problems and preferences are treated. For this reason, the notion of soft constraints has been introduced with semiring based soft constraints and valued