Flat ABAF
An ABAF is flat if assumptions cannot be derived, only assumed, i.e. every is closed. Otherwise it is non-flat.
Reference
Čyras, K., Fan, X., Schulz, C. & Toni, F. (2018). Assumption-Based Argumentation: Disputes, Explanations, Preferences. In: Baroni, P., Gabbay, D., Giacomin, M. & van der Torre, L. (eds.), Handbook of Formal Argumentation, Vol. 1, Chapter 7, pp. 365–408. College Publications.