Obligatory presupposition in discourse

Some presupposition triggers, like too, seem to be obligatory in discourses where the presupposition they induce is explicitely expressed. We show that this phenomenon concerns a larger class than is usually acknowledged, and suggest that this class corresponds to the class of presupposition triggers that have no asserted content. We then propose a pragmatic explanation relying on the neo-gricean notion of antipresupposition. We also show that the phenomenon has a complex interaction with discourse relations.