In this work, a spoken dialogue system architecture capable of dealing with Common Ground inconsistencies is proposed. Specifically, attention will be drawn upon the Conflict Search Graph, with insights on its ability to recognise problems and make them explicit via polar questions. Appropriate question forms are, indeed, adopted for the occurring type of common ground conflict, based on previous experiments, which showed that providing automatic dialogue systems with such grounding capabilities can lead to improved usability and naturalness. The described system architecture is, thus, able to detect conflicts and to use argumentation-based pragmatic strategies to signal them consistently with previous observations.