Context-free and Context-sensitive Kernels: Update and Deletion Equivalence in Abstract Argumentation

Notions of equivalence which guarantee inter-substitutability w.r.t. further modifications have received considerable interest in nonmonotonic reasoning. This paper is within the context of abstract argumentation and we focus on the most general form of a dynamic scenarios, so-called updates as well as certain sub-classes, namely local, normal and arbitrary deletions. We provide characterization theorems for the corresponding equivalence notions and draw the relations to the recently proposed kinds of expansion equivalence [15, 3]. Many of the results rely on abstract concepts like context-free kernels or semantics satisfying isolate-inclusion. Therefore, the results may apply to future semantics as well as further equivalence notions.