There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. A problem with these proposals is that they do not consider the believability of the arguments from the perspective of the intended audience. In this paper, we start by reviewing a logic-based framework for argumentation based on argument trees which provide a way of exhaustively collating arguments and counter-arguments. We then extend this framework to a model-theoretic evaluation of the believability of arguments. This extension assumes that the beliefs of a typical member of the audience for argumentation can be represented by a set of classical formulae (a beliefbase). We compare a beliefbase with each argument to evaluate the empathy (or similarly the antipathy) that an agent has for the argument. We show how we can use empathy and antipathy to define a pre-ordering relation over argument trees...