Black box AI systems for automated decision making, often based on machine learning over (big) data, map a user's features into a class or a score without exposing the reasons why. This is problematic not only for lack of transparency, but also for possible biases inherited by the algorithms from human prejudices and collection artifacts hidden in the training data, which may lead to unfair or wrong decisions. We focus on the urgent open challenge of how to construct meaningful explanations of opaque AI/ML systems, introducing the local-to-global framework for black box explanation, articulated along three lines: (i) the language for expressing explanations in terms of logic rules, with statistical and causal interpretation; (ii) the infere...