I believe, based on the notions of persuasion dialogue and negotiation dialogue that are common in the literature of non monotonic reasoning, that a notion of "persuasion" is essentially based on the "evaluation" of the arguments. Fundamentally, this is possible ONLY when agents involved in the discussion have positive and negative PREJUDICES. A prejudice is something that an agent believes true but cannot prove the truth of.
In other terms, a person would be convinced of something different form her original opinion, that is changed due to the dialogue, because one of the following facts occurs:
1) The discussant presents NEW FACTS, that the agent who is further persuaded did not know before. The introduction of these facts provides a consequence that was not believed before (and the new evidence shows that this is the case);
2) The agent presents a rule (a way of deriving things from facts) that proves a prejudice of the other agent.
An example of the first case can be a situation in which I have no prejudice about X, and a discussant provides a proof for X, based on a new fact that is introduced, and there rest of the proof is just under my control.
An example of the latter would occur when I believe not X, but have no proof of my thesis (for instance I cannot prove -X, or, more weakly, I can assert that there is no proof for X in my set of rules and facts). The discussant shows me how to prove X.
This is, in my opinion, the situation of persuasion dialogue.