Road furniture semantic labelling is vital for large scale mapping and autonomous driving systems. Much research has been investigated on road furniture interpretation in both 2D images and 3D point clouds. Precise interpretation of road furniture in mobile laser scanning data still remains unexplored. In this paper, a novel method is proposed to interpret road furniture based on their logical relations and functionalities. Our work represents the most detailed interpretation of road furniture in mobile laser scanning data. 93.3 % of poles are correctly extracted and all of them are correctly recognised. 94.3 % of street light heads are detected and 76.9 % of them are correctly identified. Despite errors arising from the recognition of other components, our framework provides a promising solution to automatically map road furniture at a detailed level in urban environments.