As on-line information services have become widespread in the Web nowadays, conversational agents appear as an effective and familiar user interface. Since conversational agents analyze the user's query based on a static process, it cannot manage complex expressions. In this paper, we propose semantic Bayesian networks that infer the user's intention based on Bayesian networks and their semantic information representing the relationship among nodes. Since conversation often contains ambiguous expressions, managing the context or the uncertainty should be necessary to support flexible conversational agents. The proposed method drives the mixed-initiative interaction (MII) that prompts for missing concepts and clarifies for spurious concepts to understand the user's intention correctly. Actually implementing a Web information guide with the proposed method, we have confirmed the usefulness of the proposed method.