Facets in Argumentation: A Formal Approach to Argument Significance

2025-05-16

AI Summary

Existing argumentation solvers lack fine-grained reasoning capabilities bridging decision and enumeration tasks, resulting in inefficient significance analysis. To address this, we introduce *facets*—a novel semantic layer situated between skeptical and credulous reasoning—that formally captures arguments that are critical yet not necessarily accepted, thereby closing the inferential gap between decision and enumeration. Theoretically, we establish the first formal definition of facet semantics and prove that its core reasoning tasks reside in P^NP, markedly lower than extension counting (#·coNP-hard). Technically, we develop a symbolic reasoning framework grounded in abstract argumentation and design a dedicated solver. Experiments on standard benchmarks demonstrate both efficiency and practicality: our approach enables real-time, interactive argument navigation and fine-grained importance assessment.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Natural Language Processing: Discourse, Pragmatics & Argument Mining

Application Category

• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Formalizing argument significance in abstract argumentation frameworks
• Bridging decision and enumeration tasks with facets concept
• Reducing complexity of reasoning between credulous and skeptical acceptance

Innovation

• Introduces facets for argument significance reasoning
• Studies complexity of facet-related tasks
• Provides implementation and experimental validation