I don’t care, I don’t know ... I know too much! On incompleteness and undecidedness in abstract argumentation

Incompleteness and undecidedness are pervasively present in human reasoning activities and make the definition of the relevant computational models challenging. In this discussion paper we focus on one such model, namely abstract argumentation frameworks, and examine several flavours of incompleteness and undecidedness thereof, by providing a conceptual analysis, a critical literature review, and some new ideas with pointers to future research.