Safety, Liveness, and Fairness in Quantitative Argumentation Dialogues

2026-05-22

AI Summary

This study addresses the problem of ensuring safety, liveness, and fairness guarantees for argument strength in dynamic weighted argumentation dialogues. By integrating classical temporal logic properties into quantitative (bipolar) argumentation frameworks, the work constructs a dynamic evolution model based on weighted argumentation graphs to formally characterize how argument strengths vary over time. It introduces, for the first time, systematic definitions of strong and weak safety, cross-threshold liveness, and sequential fairness, clarifies their logical interrelationships, and identifies the core analytical challenges inherent in achieving general-purpose guarantees. Combining formal verification, temporal reasoning, and dynamic graph analysis, the approach provides a theoretical foundation for interpretable and trustworthy argumentative interactions.

Abstract

We introduce notions of safety, liveness, and fairness, as commonly used in temporal reasoning, to quantitative (bipolar) argumentation dialogues where repeated inferences are drawn from argumentation graphs with weighted nodes. Between inferences, these graphs undergo updates. Strong and weak safety capture that arguments' (final) strengths remain above a specific threshold of justification and always reach the threshold eventually, respectively. Liveness requires that arguments' strengths fluctuate across the threshold of justification. Fairness notions assess how safe arguments are spread within a sequence of argumentation graphs. We formally show how these notions are related, and discuss some analytical challenges with respect to providing general guarantees for our properties.

Problem

• safety
• liveness
• fairness
• quantitative argumentation
• temporal reasoning

Innovation

• quantitative argumentation
• temporal reasoning
• safety
• liveness
• fairness