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Explaining predictions made by inductive classifiers has become crucial with the rise of complex models acting more and more as black-boxes. Abductive explanations are one of the most popular types of explanations that are provided for the purpose. They highlight feature-values that are sufficient for making predictions. In the literature, they are generated by exploring the whole feature space, which is unreasonable in practice. This paper solves the problem by introducing explanation functions that generate abductive explanations from a sample of instances. It shows that such functions should be defined with great care since they cannot satisfy two desirable properties at the same time, namely existence of explanations for every individual decision (success) and correctness of explanations (coherence). The paper provides a parameterized family of argumentation-based explanation functions, each of which satisfies one of the two properties. It studies their formal properties and their experimental behaviour on different datasets.