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Abstract: "In this paper I demonstrate that theories which postulate a strict tree structure of discourse on either the intentional or attentional level are not totally adequate for handling spontaneous dialogues. I use as evidence analyses of the structure of multiple headed negotiations. These are negotiation dialogues in which multiple suggestions are being negotiated at once. The question I explore in this paper is how to characterize the structure of a discourse in which multiple non-embedded adjacency pairs are initiated within a single turn since it is unclear in these cases how response parts are matched up with their corresponding initiating parts if discourse is tree structured. I argue that each non-embedded initiating part exists on a separate thread of the discourse so that an initiating part can be matched with its corresponding response part on its own thread. I develop my theory for the structure of these dialogues in the spirit of (GS86) and (Loc94). I support my claim that discourse is structured as a tapestry of interwoven threads by demonstrating that discourse level parallel structure makes it necessary to model attentional state as a graph structured stack rather than as a simple stack in order to make correct predictions about which discourse entities are readily available for pronominal reference, particularly with deictic pronouns like 'that' and 'those'. I demonstrate that the graph structured stack model is a generalization of the simple stack model and therefore covers all of the phenomena covered by the simple stack model in addition to the data discussed in this paper which is problematic for the simple stack model. An implementation of this theory is discussed in (RELED95)."