On Naive Labellings – Realizability, Construction and Patterns of Redundancy

This paper is engaged with realizability in the realm of abstract argumentation. In particular, we deal with naive labellings forming the basis for a well-established family of semantics, namely the naivity-based semantics. Consequently, characterizing this semantics is a crucial step towards delineating further naivety-based semantics such as stable and stage semantics. We provide easily verifiable criteria deciding whether a certain set of labellings can be the naive outcome of a Dungean framework. Apart from this we also present a standard construction in the affirmative case. This means, constructing a witnessing framework for a realizable set of naive labelling is possible paving the way for applications. Finally, we offer insights into representational freedom and prove a kernel-based characterization for strong equivalence, which substantially differ from its extension-based counterpart.