Aspectuality and Scalar Structure

Such aspectual verbs and degree modifiers can be treated as scalar expressions with lower-bounded (‘at least’) semantics (on scalar semantics, see Horn, 1972; Gazdar, 1979; Atlas and Levinson, 1981; Atlas, 1984; Grice, 1989; Levinson, 2000). In cases where this semantic content falls short of the informativeness and relevance expectations raised by the conversational exchange, the hearer is entitled to derive an upper-bounding implicature of the sort in (1b/2b). In other words, assuming that the speaker is trying to be cooperative and will say as much as she truthfully can that is relevant to the exchange, the fact that she chose a weaker term (e.g. start) from an informational scale gives the listener reason to think that she is not in a position to offer an informationally stronger statement (using finish) presumably because such a statement is false. In this sense, aspectual expressions resemble a variety