In everyday life, as in work situations, problem solving is a situated, accomplished process. However, few studies aim at describing this process, taking its conversational development and its logical accomplishment into account. this chapter proposes an analysis of such a process, using a theory call Interlocutory Logic. First, reasons explaining, in our point of view, the relatively few studies in this area are presented. Second, some elements of interlocutory logic are introduced. Third, an application of this theory is shown. It concerns a conversation of two experienced operators during shift changeover in a paper production company. The analysis, in taking into account the conversational process progressively, shows that these verbal exchanges permit a logical resolution of the problem and that rationality emerges from conversation. These results highlight that in situ accomplishmet of rationality is a global interactive process, including semantic, conversational and logical aspects