In Human-Machine interaction, mixed-initiative spoken dialogue systems are under investigation to allow users to speak freely to the machine. Nevertheless, natural language dialogue systems often lack the required robustness to ensure user satisfaction. A solution may lies in using a rich semantic representation and statistically modelling the dialogue sequence. This paper presents an overview of a Human-Machine dialogue system, an introduction to the statistical model of Partially Observable Markov Decision Process (POMDP) and a hierarchical semantic frame representation model. Then, an application of these two ideas is presented, using summary spaces instead of full spaces to make the computation more tractable. Some experimental results are presented, showing that this approach indeed increases system robustness. More investigations are needed to ensure practical implementations in full spaces will exhibits the same robustness.