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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…
An \textit{abstract argumentation framework} ({\sc af} for short) is a directed graph $(A,R)$ where $A$ is a set of \textit{abstract arguments} and $R\subseteq A \times A$ is the \textit{attack} relation. Let $H=(A,R)$ be an {\sc af}, $S…
In this work, we broaden the investigation of admissibility notions in the context of assumption-based argumentation (ABA). More specifically, we study two prominent alternatives to the standard notion of admissibility from abstract…
This paper presents a novel framework for structured argumentation, named extend argumentative decision graph ($xADG$). It is an extension of argumentative decision graphs built upon Dung's abstract argumentation graphs. The $xADG$…
Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments are called…
The rule $\mathrm{Defeated}(x) \leftarrow \mathrm{Attacks}(y,x),\, \neg \, \mathrm{Defeated}(y)$, evaluated under the well-founded semantics (WFS), yields a unique 3-valued (skeptical) solution of an abstract argumentation framework (AF).…
This paper introduces the notion of value-based argumentation frameworks, an extension of the standard argumentation frameworks proposed by Dung, which are able toshow how rational decision is possible in cases where arguments derive their…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
Assumption-based Argumentation (ABA) is a well-established form of structured argumentation. ABA frameworks with an underlying atomic language are widely studied, but their applicability is limited by a representational restriction to…
Dung's abstract argumentation theory can be seen as a general framework for non-monotonic reasoning. An important question is then: what is the class of logics that can be subsumed as instantiations of this theory? The goal of this paper is…
Argumentation frameworks (AFs) are a foundational tool in artificial intelligence for modeling structured reasoning and conflict. SCC-recursiveness is a well-known design principle in which the evaluation of arguments is decomposed…
Argumentation Frameworks (AFs) are a key formalism in AI research. Their semantics have been investigated in terms of principles, which define characteristic properties in order to deliver guidance for analysing established and developing…
In abstract argumentation, multiple argumentation semantics have been proposed that allow to select sets of jointly acceptable arguments from a given argumentation framework, i.e. based only on the attack relation between arguments. The…
An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the…
Abstract Dialectical Frameworks (ADFs) are argumentation frameworks where each node is associated with an acceptance condition. This allows us to model different types of dependencies as supports and attacks. Previous studies provided a…
Dung's famous abstract argumentation frameworks represent the core formalism for many problems and applications in the field of argumentation which significantly evolved within the last decade. Recent work in the field has thus focused on…
The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and…
Although various aspects of soft-constraint based norms have been explored, it is still challenging to understand preemption. Preemption is a situation where higher-level norms override lower-level norms when new information emerges. To…
In computational argumentation, gradual semantics are fine-grained alternatives to extension-based and labelling-based semantics . They ascribe a dialectical strength to (components of) arguments sanctioning their degree of acceptability.…
Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which…