Rejecting Arguments Based on Doubt in Structured Bipolar Argumentation

TL;DR

This work addresses how to model rational doubt in argumentative discourse by allowing agents to reject defended arguments and to reason about which individual sentences are accepted. It introduces Structured Bipolar Argumentation Frameworks (SBAFs) that integrate both attacks and supports between sentences, and develops two layers of semantics: coherent (strong/weak) for arguments and adequate language extensions for sentences. The semantics sit between admissible and complete in spirit and connect to existing notions such as d-admissibility and deductive support, while enabling a translation between argument-centric and sentence-centric perspectives. Through theoretical analysis and examples, the paper shows when the language view aligns with the argument view, and how strong coherence and saturation conditions influence the relationship to traditional abstract frameworks, offering a flexible, doubt-aware approach to computational argumentation.

Abstract

This paper develops a new approach to computational argumentation that is informed by philosophical and linguistic views. Namely, it takes into account two ideas that have received little attention in the literature on computational argumentation: First, an agent may rationally reject an argument based on mere doubt, thus not all arguments they could defend must be accepted; and, second, that it is sometimes more natural to think in terms of which individual sentences or claims an agent accepts in a debate, rather than which arguments. In order to incorporate these two ideas into a computational approach, we first define the notion of structured bipolar argumentation frameworks (SBAFs), where arguments consist of sentences and we have both an attack and a support relation between them. Then, we provide semantics for SBAFs with two features: (1) Unlike with completeness-based semantics, our semantics do not force agents to accept all defended arguments. (2) In addition to argument extensions, which give acceptable sets of arguments, we also provide semantics for language extensions that specify acceptable sets of sentences. These semantics represent reasonable positions an agent might have in a debate. Our semantics lie between the admissible and complete semantics of abstract argumentation. Further, our approach can be used to provide a new perspective on existing approaches. For instance, we can specify the conditions under which an agent can ignore support between arguments (i.e. under which the use of abstract argumentation is warranted) and we show that deductive support semantics is a special case of our approach.

Figures (2)

• Figure 1: $SCA$: strongly coherent argument extensions, $WCA$: weakly coherent argument extensions, $WAL$: weakly adequate language extensions, $SAL$: strongly adequate language extensions. $\mathit{SCA}\subseteq\mathit{WCA}$ indicates that each strongly coherent extension is also weakly coherent. "$\subseteq^*$" relates argument extensions with the argument sets of language extensions. Dashed relations only hold in saturated SBAFs.
• Figure 2: $\{a_1\}$ is strongly coherent if we disregard arguments $a_2$ and $a_3$. However, in the presence of those arguments, accepting $a_1$ would, by strong support-closure, require to accept both $a_2$ and $a_3$. But then the extension would not be conflict-free. Thus, there is no strongly coherent extension containing $a_1$ in the full framework.

Theorems & Definitions (80)

• Example 1
• Example 2
• Definition 1: Abstract Argumentation Framework
• Definition 2: Language
• Example 3
• Definition 3: Arguments
• Example 4
• Definition 4: Support and Attack
• Example 5
• Definition 5: Structured Bipolar Argumentation Framework