Wolfgang Dvorak

Michael Bernreiter, Wolfgang Dvorak, Anna Rapberger et al.

In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on claim-level rather than on the argument-level, while under certain natural restrictions (arguments with the same claims have the same outgoing attacks) these properties are conserved. We now investigate these effects when, in addition, preferences have to be taken into account and consider four prominent reductions to handle preferences between arguments. As we shall see, these reductions give rise to different classes of claim-augmented argumentation frameworks, and behave differently in terms of semantic properties and computational complexity. This strengthens the view that the actual choice for handling preferences has to be taken with care.

Giovanni Buraglio, Wolfgang Dvorak, Stefan Woltran

Strong equivalence between knowledge bases ensures the possibility of replacing one with the other without affecting reasoning outcomes, in any given context. This makes it a crucial property in nonmonotonic formalisms. In particular, the fields of logic programming and abstract argumentation provide primary examples in which this property has been subject to vast investigations. However, while (classes of) logic programs and abstract argumentation frameworks are known to be semantically equivalent in static settings, this alignment breaks in dynamic contexts due to differing notions of update. As a result, strong equivalence does not always carry over from one formalism to the other. In this paper, we carefully investigate this discrepancy and introduce a new notion of strong equivalence for logic programs. Our approach preserves strong equivalence under translation between certain classes of logic programs and both Dung-style and claim-augmented argumentation frameworks, thus restoring compatibility across these formalisms.

Giovanni Buraglio, Wolfgang Dvorak, Stefan Woltran

Assumption-Based Argumentation (ABA) is a well-established formalism for modelling and reasoning over debates, with a wide range of applications. However, the high computational complexity of core reasoning tasks in ABA poses a significant challenge for its applicability. This issue is further aggravated when ABA frameworks (ABAFs) are instantiated into graph-based argumentation formalisms, such as Dung's Argumentation Frameworks (AFs) and Argumentation Frameworks with Collective Attacks (SETAFs). In knowledge representation and reasoning, a key strategy to address computational intractability is to optimise reasoning over a given knowledge base through divide-and-conquer algorithms. A paradigmatic example of this approach is splitting, where extensions of a given framework are computed incrementally, by restricting the search space to sub-frameworks only, and then combining the obtained results. This approach has been successfully applied to AFs, for which also a parametrised version has been introduced under stable semantics. However, the exponential growth produced by the instantiation might undermine the usefulness of splitting on the argument graphs induced by ABAFs. To address this issue, our work investigates the concept of splitting on the knowledge base rather than on its graph-based instantiation. Furthermore, we generalise splitting to its parametrised version for ABAFs.

Wolfgang Dvorak, Stefan Woltran

Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms of different semantics proposed for abstract argumentation frameworks, a nonmonotonic yet simple formalism which received increasing interest within the last decade. Although the properties of these different semantics are nowadays well understood, there are no explicit results about intertranslatability. We provide such translations wrt. different properties and also give a few novel complexity results which underlie some negative results.