Characterizing Equivalence Notions for Labelling-Based Semantics

A central question in knowledge representation is the following: given some knowledge representation formalism, is it possible, and if so how, to simplify parts of a knowledge base without affecting its meaning, even in the light of additional information? The term strong equivalence was coined in the literature, i.e. strongly equivalent knowledge bases can be locally replaced by each other in a bigger theory without changing the semantics of the latter. In contrast to classical (monotone) logics where standard and strong equivalence coincide, it is possible to find ordinary but not strongly equivalent objects for any nonmonotonic formalism available in the literature. This paper addresses these questions in the context of abstract argumentation theory. Much effort has been spent to characterize several argumentation tailored equivalence notions w.r.t. extension-based semantics. In recent times labelling-based semantics have received increasing attention, for example in connection with algorithms computing extensions, proof procedures, dialogue games, dynamics in argumentation as well as belief revision in general. Of course, equivalence notions allowing for replacements are of high interest for the mentioned topics. In this paper we provide kernel-based characterization theorems for semantics based on complete labellings as well as admissible labellings w.r.t. eight different equivalence notions including the aforementioned most prominent one, namely strong equivalence.