Minimality, necessity and sufficiency for argumentation and explanation

We discuss explanations for formal (abstract and structured) argumentation – the question whether and why a certain argument or claim can be accepted (or not) under various extension-based semantics. We introduce a flexible framework, which can act as the basis for many different types of explanations. For example, we can have simple or comprehensive explanations in terms of arguments for or against a claim, arguments that (indirectly) defend a claim, the evidence (knowledge base) that supports or is incompatible with a claim, and so on. We show how selection based on necessity and sufficiency can be captured in our basic framework and discuss a real-life application.