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Explanations in Machine Learning come in many forms, but a consensus regarding their desired properties is yet to emerge. In this paper we introduce a taxonomy and a set of descriptors that can be used to characterise and systematically assess explainable systems along five key dimensions: functional, operational, usability, safety and validation. In order to design a comprehensive and representative taxonomy and associated descriptors we surveyed the eXplainable Artificial Intelligence literature, extracting the criteria and desiderata that other authors have proposed or implicitly used in their research. The survey includes papers introducing new explainability algorithms to see what criteria are used to guide their development and how these algorithms are evaluated, as well as papers proposing such criteria from both computer science and social science perspectives. This novel framework allows to …