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.
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.
Argumentation games, which model reasoning as adversarial dialogue, offer intuitive and explainable mechanisms for decision-making in AI. However, their implementation has lagged behind inference-focused approaches, particularly in structured argumentation frameworks like assumption-based argumentation (ABA). This work presents, to our knowledge, the first application of multi-shot answer set programming (ASP) for implementing argument games, focusing on ABA dispute derivations. Leveraging a recent rule-based representation of ABA disputes, our method combines a declarative program with lightweight script-based control of multi-shot aspects, yielding a modular and adaptable system. We extend this core approach to support alternative games and show how it can also be used to implement argument games for Dung’s abstract argumentation formalism. Empirical results show that our implementation outperforms existing ABA dispute systems. We also introduce an approximate variant that further improves efficiency – reaching the level of the best inference-focused ABA system – while maintaining perfect specificity (true negative rate), demonstrating the practical value of multi-shot ASP, especially in interactive, explainable settings.
Weighted-knowledge bases and cost-based semantics represent a recent formalism introduced by Bienvenu et al. for Ontology Mediated Data Querying in the case where a given knowledge base is inconsistent. This is done by adding a weight to each statement in the knowledge base (KB), and then giving each DL interpretation a cost based on how often it breaks rules in the KB. In this paper we compare this approach with c-representations, a form of non-monotonic reasoning originally introduced by Kern-Isberner. c-Representations describe a means to interpret defeasible concept inclusions in the first-order case. This is done by assigning a numerical ranking to each interpretations via penalties for each violated conditional. We compare these two approaches on a semantic level. In particular, we show that under certain conditions a weighted knowledge base and a set of defeasible conditionals can generate the same ordering on interpretations, and therefore an equivalence of semantic structures up to relative cost. Moreover, we compare entailment described in both cases, where certain notions are equivalently expressible in both formalisms. Our results have the potential to benefit further work on both cost-based semantics and c-representations
