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In this paper, we describe an architecture for conversational systems that enables human-like performance along several important dimensions. First, interpretation is incremental, multi-level, and involves both general and task- and domain-specific knowledge. Second, generation is also incremental, proceeds in parallel with interpretation, and accounts for phenomena such as turn-taking, grounding and interruptions. Finally, the overall behavior of the system in the task at hand is determined by the (incremental) results of interpretation, the persistent goals and obligations of the system, and exogenous events of which it becomes aware. As a practical matter, the architecture supports a separation of responsibilities that enhances portability to new tasks and domains.