Rejecting Arguments Based on Doubt in Structured Bipolar Argumentation

TL;DR

This paper introduces structured bipolar argumentation frameworks that incorporate doubt-based rejection and sentence-level acceptance, offering a nuanced semantics that better models realistic debate positions.

Contribution

It develops a novel computational approach integrating doubt-based rejection and sentence acceptance, extending existing argumentation semantics with new language and agent position representations.

Findings

Semantics do not force acceptance of all defended arguments.

Provides semantics for acceptable sets of sentences.

Shows deductive support semantics as a special case.

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.