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 have a consensus among medical professionals is not feasible and might even be regarded as counterproductive. In this paper, we introduce an approach for expressing 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. Indeed, a lattice of agreement degrees can show evidence about whether or not it is acceptable to dismiss goals in order to maximize agreements regarding other goals.