The service robot supports people in their daily activities, while the interaction between humans and robots seems to be an important part of its performance. Dialogue may be beneficial to the robot to increase the flexibility and facility of the interaction. Traditional robots have merely dealt with simple queries like commands, but in conversation people often omit some words because of the background knowledge or the context of the conversation. Since environments contain various uncertainties, managing the context of a dialogue or the uncertainties should be necessary to support smarter service robots. In order to establish a natural communication between people and robots, we have been investigating the use of mixed-initiative interaction that prompts for missing concepts and clarifies for spurious concepts. Hierarchically designed Bayesian networks are presented for the mixed-initiative interaction. A simulation and a real robot are constructed for the demonstration of the proposed method, and experiments also show the usefulness.