In this paper, it is shown how formal dialectic can be extended to model multi-agent argumentation in which each participant is an agent. An agent is viewed as a participant in a dialogue who not only has goals, and the capability for actions, but who also has stable characteristics of types that can be relevant to an assessment of some of her arguments used in that dialogue. When agents engage in argumentation in dialogues, each agent has a credibility function that can be adjusted upwards or downwards by certain types of arguments brought forward by the other agent in the dialogue. One type is the argument against the person or argumentum ad hominem, in which personal attack on one party’s character is used to attack his argument. Another is the appeal to expert opinion, traditionally associated with the informal fallacy called the argumentum ad verecundiam. In any particular case, an agent will begin a dialogue with a given degree of credibility, and what is here called the credibility function will affect the plausibility of the arguments put forward by that agent. In this paper, an agent is shown to have specific character traits that are vital to properly judging how this credibility function should affect the plausibility of her arguments, including veracity, prudence, sincerity and openness to opposed arguments. When one of these traits is a relevant basis for an adjustment in a credibility function, there is a shift to a subdialogue in which the argumentation in the case is re-evaluated. In such a case, it is shown how the outcome can legitimately be a reduction in the credibility rating of the arguer who was attacked. Then it is shown how the credibility function should be brought into an argument evaluation in the case, yielding the outcome that the argument is assigned a lower plausibility value.