In many real applications, to reach an agreement between the participants of a dialogue, which can be for instance a negotiation, is not easy. Indeed, there are application domains such as the medical domain where to reach a consensus among medical professionals is not feasible and might be even regarded as counterproductive. In this paper, we introduce an approach for expressing qualitative preferences between the goals of a dialogue considering ordered disjunction rules. By applying argumentation semantics and degrees of satisfaction of goals, we introduce the so-called dialogue agreement degree. Moreover, by considering sets of dialogue agreement degrees, we define a lattice of agreement degrees. We argue that a lattice of agreement degrees suggests different approximations between the current state of a dialogue and its aimed goals; hence, a lattice of agreement degrees can help to define different heuristics in the settings of strategic argumentation.
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