Tree Discourse Grammar or How to Get Attached to a Discourse?

In this paper I describe a discourse grammar which is based on a further development of a Tree Adjoining Grammar (TAG). Adding features and the restriction that a newly processed sentence can only be added on the right frontier of the discourse tree, I follow Gardent's description of a Tree Insertion Grammar (TIG). I extend this formalism with respect to world and contextual knowledge, using a non-monotonic reasoning system similar to Lascarides and Asher (1993). The rhetorical relations are represented by a constrained sort hierarchy which allows a precise deenition of the semantics{pragmatics interface for discourse processing. Moreover, the attachment to an already processed discourse can be explained by the restriction of the discourse tree.