  Through the General Data Protection Regulation (GDPR), the European Union has
set out its vision for Automated Decision- Making (ADM) and AI, which must be
reliable and human-centred. In particular we are interested on the Right to
Explanation, that requires industry to produce explanations of ADM. The
High-Level Expert Group on Artificial Intelligence (AI-HLEG), set up to support
the implementation of this vision, has produced guidelines discussing the types
of explanations that are appropriate for user-centred (interactive) Explanatory
Tools. In this paper we propose our version of Explanatory Narratives (EN),
based on user-centred concepts drawn from ISO 9241, as a model for user-centred
explanations aligned with the GDPR and the AI-HLEG guidelines. Through the use
of ENs we convert the problem of generating explanations for ADM into the
identification of an appropriate path over an Explanatory Space, allowing
explainees to interactively explore it and produce the explanation best suited
to their needs. To this end we list suitable exploration heuristics, we study
the properties and structure of explanations, and discuss the proposed model
identifying its weaknesses and strengths.
