The idea that aspectuality, roughly, the property which makes it possible for a sentence to signal whether or not it pertains to something bounded, can be characterized compositionally by a system of rules of interpretation has been around for some time now. However, its articulation appears to be difficult. Not only is it an area of investigation in which several disciplines are deeply involved – linguistics, logic, cognitive science, computer science and philosophy – the phenomena are also very hard to capture because the systematic formal study of temporality as expressed by sentences of natural languages is relatively new. Of course, there is a tradition in which at least a lot of valuable data and generalizations have been made available. However, when it comes to making a theory, soon one is bound to recognize that a lot of preparatory work is to be done before one can even think about theory formation. The picture is also complicated by the fact that the formal semantic study of discourse structure has developed very rapidly in the past ten years, so that all of a sudden all sorts of relatively new factors are drawn into an area of investigation whose scope was mostly restricted to sentences only. A lot of sorting out has to be done against the currents of shifting fashions.