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This paper describes a novel, principled approach to real-valued dataset reduction based on fuzzy and rough set theory. The approach is based on the formulation of fuzzy-rough discernibility matrices, that can be transformed into a satisfiability problem; an extension of rough set approaches that only apply to discrete datasets. The fuzzy-rough hybrid reduction method is then realised algorithmically by a modified version of a traditional satisifability approach. This produces an efficient and provably optimal approach to data reduction that works well on a number of machine learning benchmarks in terms of both time and classification accuracy.