The Philips automatic telephone switchboard and directory information system PADIS provides a natural-language user interface to a telephone directory database. Using speech recognition and language understanding technologies, the system offers phone numbers, fax numbers, email addresses, and room numbers as well as direct call completion to a desired party. In this paper, we present the underlying probabilistic framework, the system architecture, and the individual modules for speech recognition, language understanding, dialogue control, and speech output. In addition, we report results on performance and user behaviour obtained from a field test in our research lab with a 600-entry database. We derive a new maximum-a-posteriori decision rule which incorporates database knowledge and dialogue history as constraints in speech recognition and language understanding. It has improved speech understanding accuracy by 19 % (in terms of concept error rate), and reduced attribute substitution errors (e.g. recognition of a wrong name) by 38%. The decision rule is implemented in a multi-stage approach as a combination of state-of-the-art speech recognition, partial parsing with an attributed stochastic context-free grammar, and an N-best algorithm which is also described in this paper. The system conducts a flexible mixed-initiative dialogue rather than using a rigid form-filling scheme, and incorporates database knowledge to optimize the dialogue flow.