The process of adding to the common ground between conversational
participants (called grounding) has previously been either
oversimplified or studied in an off-line manner. I will present a
computational theory, based on speech act theory, in which, for any
given state of the conversation, judgments can be made as to whether
material has been grounded or what further utterance types are needed
to ground the material. I relate this theory to the mental states of
participating agents, showing the motivations for performing
particular acts and what their effects will be. Also, I will show how
this theory has been used by the TRAINS-93 natural language
conversation system as part of the dialogue management strategy.