Quantitative Bipolar Argumentation Frameworks : Explanations for Safety, Liveness, and Fairness

Sammanfattning

We introduce formal explanations for the notions of safety, liveness, and fairness in quantitative (bipolar) argumentation dialogues where repeated inferences are drawn from argumentation graphs with weighted nodes. While these properties allow us to evaluate the stability, fluctuations, and equity of arguments across a dialogue chain, there is a lack of formal methods for explaining why a property is satisfied or violated. We introduce and analyse the definitions of naive, suffi-cient, counter factual, and minimal explanations for safety, liveness, and fairness properties in chains of quantitative bipolar argumentation frameworks. Focusing on acyclic expansion chains, we investigate the structural properties of these explanations, proving that while naive explanations are complete but not sound, sufficient and counter factual explanations achieve both soundness and completeness. By identifying the minimal set of arguments outside a topic set responsible for a property’s status, this thesis provides a mechanism to justify and audit there liability and fairness of dynamic argumentation dialogues.