In this paper we present the basic principles underlying the DenK-system, a generic cooperative interface combining linguistic and visual interaction. The system integrates results from fundamental research in knowledge representation, communication, natural language semantics and pragmatics, and object-oriented animation. Our design incorporates a cooperative and knowledgeable electronic assistant that communicates with a user in natural language, and an application domain, which is presented visually. The assistant, that we call thecooperator, has an information state that is represented in a rich form of Type Theory, a formalism that enables us to model the inherent cognitive dynamics of a dialogue participant. Pragmatic issues in man-machine interaction, concerning the use of natural language and knowledge in cooperative communication, are central to our approach.