Let us see how we can model discourse understanding using tableaux-based model generation. Up to now, we've only looked at single sentences, but we will show that it presents no problem in principle for our tableaux-based method to process multiple sentences incrementally. For simplicity we shall simply take a discourse to be a sequence of single sentences, disregarding facets such as anaphora, presupposition, or rhetorical structure. Even using this simplistic abstraction, we have quite some interesting problems to solve.