There is a small CS/AI community that works on "argumentation", putting exactly the problems you describe in symbols. For anyone who is interested in the detail

There is a small CS/AI community that works on "argumentation", putting exactly the problems you describe in symbols. For anyone who is interested in the details, there are several books on the topic, for example the "Handbook of Formal Argumentation" by Baroni et al. I concede that formal argumentation is--as far as I know--still waiting to be applied in large-scale scenarios.