We introduce notions of safety, liveness, and fairness, as commonly used in temporal reasoning and distributed systems, to quantitative (bipolar) argumentation dialogues where repeated inferences are drawn from argumentation graphs with weighted nodes. Between inferences, these graphs undergo updates. Safety and liveness captures that arguments' (final) strengths attain a specific threshold of credibility and always attain the threshold eventually, respectively. Fairness notions assess how safe arguments are spread within a sequence of argumentation graphs. Additionally, we introduce the notion of oscillation to capture the stability of a topic argument with respect to the threshold of credibility. We formally show how these notions are related, and discuss some analytical challenges with respect to providing general guarantees for our properties.

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