Comparative Expressivity for Structured Argumentation Frameworks with Uncertain Rules and Premises

2025-10-21

AI Summary

This study addresses the modeling of qualitative uncertainty in rules and premises within structured argumentation frameworks, systematically comparing the expressive capabilities of abstract versus structured argumentation models for representing uncertainty. Method: We introduce a formal notion of expressiveness to uniformly characterize both frameworks, propose the first structured argumentation model based on ASPIC+ that incorporates uncertain rules and premises, and conduct a formal analysis using incomplete abstract frameworks alongside their dependency-based extensions. Contribution/Results: We establish key positive and negative expressiveness results—precisely delineating the translatability boundary, inherent limitations, and complementary strengths between abstract and structured models in representing uncertainty. These findings not only advance the theoretical foundations of uncertain argumentation but also provide a novel paradigm for modeling complex, qualitative uncertainty in applied domains such as trustworthy AI and legal reasoning.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Knowledge Representation and Reasoning: Argumentation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on extit{abstract} models for arguing with uncertainty. Following a recent trend in the literature, we tackle the open question of studying plausible instantiations of these abstract models. To do so, we ground the uncertainty of arguments in their components, structured within rules and premises. Our main technical contributions are: i) the introduction of a notion of expressivity that can handle abstract and structured formalisms, and ii) the presentation of both negative and positive expressivity results, comparing the expressivity of abstract and structured models of argumentation with uncertainty. These results affect incomplete abstract argumentation frameworks, and their extension with dependencies, on the abstract side, and ASPIC+, on the structured side.

Problem

• Modeling qualitative uncertainty in structured argumentation frameworks
• Comparing expressivity of abstract versus structured argumentation models
• Analyzing uncertainty in argument components like rules and premises

Innovation

• Modeling uncertainty in structured argumentation frameworks
• Introducing expressivity notion for abstract and structured formalisms
• Comparing expressivity of argumentation models with uncertainty