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In this paper we explore a new theory of discourse structure that stresses the role of purpose and processing in discourse. In this theory, discourse structure is composed of three separate but interrelated components: the structure of the sequence of utterances (called the linguistic structure), a structure of purposes (called the intentional structure), and the state of focus of attention (called the attentional state). The linguistic structure consists of segments of the discourse into which the utterances naturally aggregate. The intentional structure captures the discourse-relevant purposes, expressed in each of the linguistic segments as well as relationships among them. The attentional state is an abstraction of the focus of attention of the participants as the discourse unfolds. The attentional state, being dynamic, records the objects, properties, and relations that are salient at each point of the discourse. The distinction among these components is essential to provide an adequate explanation of such discourse phenomena as cue phrases, referring expressions, and interruptions. The theory of attention, intention, and aggregation of utterances is illustrated in the paper with a number of example discourses. Various properties of discourse are described, and explanations for the behavior of cue phrases, referring expressions, and interruptions are explored. This theory provides a framework for describing the processing of utterances in a discourse. Discourse processing requires recognizing how the utterances of the discourse aggregate into segments, recognizing the intentions expressed in the discourse and the relationships among intentions, and tracking …