As observed before, the present aspectual theory focusses on the interaction between temporal and atemporal structure in sentences like (1)–(4). This interaction can be (crudely and provisionally) captured by an aspectual ‘feature algebra’ based on two parameters discussed above and collected in Figure 8. However appealing this compositional machinery may be, it fails to give a satisfactory account of why it is that an NP is [+sqa] or [-sqa]. For example, to assign [+sqa] to both a sandwich and three sandwiches is correct but it does not explain anything unless we know what these NPs share. This extends, of course, to NPs like many sandwiches, at least three sandwiches, most sandwiches, etc. which also may express [+sqa]-information. A detailed enquiry is also necessary because certain NPs look as if they are [+sqa], whereas they are to be interpreted as [-sqa]. One needs to know more about the NPs themselves in order to make sure that the process of compositional interpretation proceeds as it should. Therefore, Part II will focus on the atemporal side of Figure 8. Two results are aimed at. The first one is to indicate exactly under which conditions NPs are [+sqa] or [-sqa]. This means that the representation of NPs should contain or lack certain information which is interpreted as contributing to terminative or durative aspect. The second one is to indicate exactly where atemporal structure ‘meets’ temporal structure.