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.

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