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This paper proposes the use of Belief Networks (BN) for mixed-initiative dialog modeling. The BN-based framework was previously used for natural language understanding, where BNs infer the informational goal of the user's query based on its parsed semantic concepts. We extended this framework with the technique of backward inference that can automatically detect missing or spurious concepts based on the inferred goal. This is, in turn, used to drive the mixed-initiative dialog model that prompts for missing concepts and clarifies for spurious concepts. Applicability is demonstrated for a simple foreign exchange domain, and our framework's mixed-initiative interactions were shown to be superior to the system-initiative and user-initiative interactions. We also investigate the scalability and portability of the BN-based framework to the more complex air travel (ATIS) domain. Backward inference detected an increased number of missing and spurious concepts, which led to redundancies in the dialog model. We experimented with several remedial measures that showed promise in reducing the redundancies. We also present a set of principles for hand-assigning "degrees of belief" to the BN to reduce the demand for massive training data when porting to a new domain. Experimentation with the ATIS data also gave promising results.