 The discourse update of the completed program (54) yields that at some point after \(t\) John will achieve the culmination and will have run one mile (see van Lambalgen and Hamm 2005: 61ff. for a proof). Obviously, the same integrity constraint in combination with the activity in (55a) only licenses the inferences that there was some past running activity. In the case of an accomplishment the course of events dramatically changes if we add information to the representation as in (56b). Now, both (56a) and (56b) only allow the inference that there was a running event but, arguably, John didn’t reach his goal in (56b). Without going into further details it should be clear how this non-monotonic inference works. The derivation works analogously to the simpler instances of the frame problem discussed above. 