  The field of explainable AI (XAI) has quickly become a thriving and prolific
community. However, a silent, recurrent and acknowledged issue in this area is
the lack of consensus regarding its terminology. In particular, each new
contribution seems to rely on its own (and often intuitive) version of terms
like "explanation" and "interpretation". Such disarray encumbers the
consolidation of advances in the field towards the fulfillment of scientific
and regulatory demands e.g., when comparing methods or establishing their
compliance with respect to biases and fairness constraints. We propose a
theoretical framework that not only provides concrete definitions for these
terms, but it also outlines all steps necessary to produce explanations and
interpretations. The framework also allows for existing contributions to be
re-contextualized such that their scope can be measured, thus making them
comparable to other methods. We show that this framework is compliant with
desiderata on explanations, on interpretability and on evaluation metrics. We
present a use-case showing how the framework can be used to compare LIME, SHAP
and MDNet, establishing their advantages and shortcomings. Finally, we discuss
relevant trends in XAI as well as recommendations for future work, all from the
standpoint of our framework.
