Facets in Argumentation: A Formal Approach to Argument Significance

TL;DR

This paper introduces facets in argumentation frameworks, a new concept for nuanced reasoning about argument significance, which simplifies certain computational tasks and aids user comprehension.

Contribution

The paper proposes the novel concept of facets in argumentation frameworks, bridging decision and enumeration, and analyzes their complexity and practical feasibility.

Findings

Tasks involving facets are computationally easier than counting extensions.

Facets help users navigate and understand argument significance.

Implementation and experiments demonstrate the approach's feasibility.

Abstract

Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the relationship between them, such as stable or admissible. Today's solvers implement tasks such as finding extensions, deciding credulous or skeptical acceptance, counting, or enumerating extensions. While these tasks are well charted, the area between decision, counting/enumeration and fine-grained reasoning requires expensive reasoning so far. We introduce a novel concept (facets) for reasoning between decision and enumeration. Facets are arguments that belong to some extensions (credulous) but not to all extensions (skeptical). They are most natural when a user aims to navigate, filter, or comprehend the significance of specific arguments, according to their needs. We study the complexity and show that tasks involving facets are much easier than counting extensions. Finally, we provide an implementation, and conduct experiments to demonstrate feasibility.