This work proposes novel splitting techniques for argumentation formalisms that incorporate supports between defeasible elements. We base our studies on Bipolar Set-Based Argumentation Frameworks (BSAFs), which generalize argumentation frameworks with collective attacks (SETAFs), as well as Bipolar Argumentation Frameworks (BAFs), by incorporating both collective attacks and supports. Notably, BSAFs establish a crucial link to structured argumentation as they naturally capture general (potentially non-flat) assumption-based argumentation. The increase in expressiveness calls for diverse forms of splitting. We consider splits over collective attacks (thereby generalizing the recently proposed splitting techniques for SETAFs), splits over collective supports, as well as splits over both collective attacks and supports. We establish suitable splitting schemata and prove their correctness for the most common argumentation semantics.

We introduce a notion of conditional independence in (flat) assumption-based argumentation (ABA), where independence between (sets of) assumptions amounts to the presence of information about one set of assumptions not impacting the acceptability of another. We study general properties, computational complexity, and the relation to independence in abstract argumentation. In light of the high computational complexity of deciding independence, we introduce sound methods for checking independence in polynomial time via two different routes: the first utilizes the strongly connected components (SCCs) of the instantiated abstract argumentation framework; the second exploits the structure of the ABA framework directly. Along the way, we introduce the notion of SCC-recursiveness for ABA.

In this work, we broaden the investigation of admissibility notions in the context of assumption-based argumentation (ABA). More specifically, we study two prominent alternatives to the standard notion of admissibility from abstract argumentation, namely strong and weak admissibility, and introduce the respective preferred, complete and grounded semantics for general (sometimes called non-flat) ABA. To do so, we use abstract bipolar set-based argumentation frameworks (BSAFs) as formal playground since they concisely capture the relations between assumptions and are expressive enough to represent general non-flat ABA frameworks, as recently shown. While weak admissibility has been recently investigated for a restricted fragment of ABA in which assumptions cannot be derived (flat ABA), strong admissibility has not been investigated for ABA so far. We introduce strong admissibility for ABA and investigate desirable properties. We furthermore extend the recent investigations of weak admissibility in the flat ABA fragment to the non-flat case. We show that the central modularization property is maintained under classical, strong, and weak admissibility. We also show that strong and weakly admissible semantics in non-flat ABA share some of the shortcomings of standard admissible semantics and discuss ways to address these.

We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics σ and τ, refines σ (base condition) by accepting only those σ-extensions that have no non-empty τ-extension in their reduct (vacuity condition). We give a systematic overview on vacuous reduct semantics resulting from combining different admissibility-based and conflict-free semantics and present a principle-based analysis of vacuous reduct semantics in general. We provide criteria for the inheritance of principle satisfaction by a vacuous reduct semantics from its base and vacuity condition for established as well as recently introduced principles in the context of weak argumentation semantics. We also conduct a principle-based analysis for the special case of undisputed semantics.

Is an argument acceptable if all potential counter-arguments are unacceptable themselves? In standard models of argumentation, the answer to this question is counter-intuitively not necessarily yes. However, based on the notion of weak admissibility, a family of semantics has been established where these unreasonable attacks do not successfully counter otherwise strong arguments. While in the abstract setting weak admissibility is well-understood, a similar issue arises in the context of structured argumentation formalisms like assumption based argumentation (ABA). It is well known that under standard argumentation semantics, ABA frameworks can be reduced to abstract argumentation frameworks (AFs), however, it turns out that in the case of weak admissibility this approach surprisingly fails. We instead propose to utilize a recently published instantiation technique utilizing collective attacks (SETAFs). We first define weak admissibility for SETAFs and study basic properties; afterwards, we push our proposal to the structured setting. We show that via our approach the characteristic properties of weak admissibility carry over to ABA, and thus establish a basis for further studies of these common scenarios also in ABA and related structured argumentation formalisms.

We consider the recently introduced vacuous reduct semantics in abstract argumentation that allows the composition of arbitrary argumentation semantics through the notion of the reduct. We show that by recursively applying the principle of vacuous reduct semantics we are able to cover a broad range of semantical approaches. Our main result shows that we can recover the weakly preferred semantics as the unique solution of a fixed point equation involving an infinite application of the vacuous reduct semantics based only on the very simple property of conflict-freeness. We also conduct an extensive study of the computational complexity of the recursive application of vacuous reduct semantics, which shows that it completely covers each level of the polynomial hierarchy, depending on the recursion depth.

We revisit the foundations of ranking semantics for abstract argumentation frameworks by observing that most existing approaches are incompatible with classical extension-based semantics. In particular, most ranking semantics violate the principle of admissibility, meaning that admissible arguments are not necessarily better ranked than inadmissible arguments. We propose new postulates for capturing said compatibility with classical extension-based semantics and present a new ranking semantics that complies with these postulates. This ranking semantics is based on the recently proposed notion of serialisability that allows to rank arguments according to the number of conflicts needed to be solved in order to include that argument in an admissible set.