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.

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.

The topic of forgetting, which loosely speaking means losing, removing, or even hiding some variables, propositions, or formulas, has been extensively studied in the field of knowledge representation and reasoning for many major formalisms. In this article, we convey this topic to the highly active field of abstract argumentation. We provide an in-depth analysis of desirable syntactical and/or semantical properties of possible forgetting operators. In doing so, we included well-known logic programming conditions, such as strong persistence or strong invariance. Further, we argue that although abstract argumentation and logic programming are closely related, it is not possible to reduce forgetting in abstract argumentation to forgetting in logic programming in a straightforward manner. The analysis of desiderata, adapted to the specifics of abstract argumentation, includes implications among them, individual and collective satisfiability, and identifying inherent limits for a set of prominent semantics. Finally, we conduct a case study on stable semantics incorporating concrete forgetting operators.

While the flat fragment of assumption-based argumentation (ABA) is widely studied in the literature, the general, non-flat case has mostly been neglected so far. Until recently, there was no possible way to instantiate non-flat ABA in terms of an abstract argumentation framework. While this gap has been closed for complete-based ABA semantics, capturing admissible-based semantics cannot yet be achieved by looking at the relation between the instantiated arguments only; it requires augmenting arguments with their premises, hence being a semi-abstract instantiaiton. In this paper, we provide a compact and fully abstract instantiation by making use of both collective attack and support relations. Then, inspired by fundamental properties of abstract formalisms, we identify flaws of native ABA semantics in the non-flat case and provide refinements thereof, utilizing our novel instatiation.

We address the issue of forgetting in assumption-based argumentation (ABA). Forgetting is driven by the goal to remove certain elements from a knowledge base, while preserving the structure of its models as well as possible. We introduce several forgetting operators tailored to accomplish the removal of different pieces of the ABA knowledge base—assumptions, contraries, and atoms—formalizing a diverse selection of perspectives on this issue. We examine the quality of our operators by studying their compliance with suitable desiderata we propose. Thereby, we investigate the impact of the operators on the syntax of the given ABA knowledge base, its semantics, but also the instantiated argumentation framework; thus bridging recent forgetting studies on non-monotonic formalisms including argumentation theory.

The topic of forgetting has been extensively studied in the field of knowledge representation and reasoning for many major formalisms. Quite recently it has been introduced to abstract argumentation. However, many already known as well as essential aspects about forgetting like strong persistence or strong invariance have been left unconsidered. We show that forgetting in abstract argumentation cannot be reduced to forgetting in logic programming. In addition, we deal with the more general problem of forgetting whole sets of arguments and show that iterative application of existing operators for single arguments does not necessarily yield a desirable result as it may not produce an informationally economic argumentation framework. As a consequence we provide a systematic and exhaustive study of forgetting desiderata and associated operations adapted to the intrinsics of abstract argumentation. We show the limits and shed light on the possibilities.

Abstract Whereas the operation of forgetting has recently seen a considerable amount of attention in the context of Answer Set Programming (ASP), most of it has focused on theoretical aspects, leaving the practical issues largely untouched. Recent studies include results about what sets of properties operators should satisfy, as well as the abstract characterization of several operators and their theoretical limits. However, no concrete operators have been investigated. In this paper, we address this issue by presenting the first concrete operator that satisfies strong persistence – a property that seems to best capture the essence of forgetting in the context of ASP – whenever this is possible, and many other important properties. The operator is syntactic, limiting the computation of the forgetting result to manipulating the rules in which the atoms to be forgotten occur, naturally yielding a forgetting result that is close to the original program.