Extension Removal in Abstract Argumentation: Necessary and Sufficient Conditions

In the research on dynamics of abstract argumentation frameworks, Baumann et al. proposed the extension removal problem for the first time in 2019 and provided an axiomatization of removal operators. In contrast, we are interested in how to solve the extension removal problem in practice. Our consideration includes designing a special removal operator for preventing undesired extensions from being accepted whatsoever in the modified AF; and limiting AF modification to normal expansion so as to honor the original arguments and their attacks. The contribution of this paper consists of four jointly necessary and sufficient conditions identified for solving the extension removal problem under preferred, stable, semi-stable, grounded, ideal and complete semantics, as well as an impossibility conclusion under naive semantics. Such conditions are both minimum and absolute which can be used to determine when the removal problem is (un)solvable.