Ideal Semantics (ABA)

A set of assumptions $S \subseteq \mathcal{A}$ is ideal iff $S$ is $\subseteq$ -maximal among the admissible sets that are contained in every preferred extension.

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.