In this paper I provide an analysis of at least that derives the epistemic and concessive interpretations of utterances containing at least (discussed in Nakanishi & Rullmann 2009) from a single denotation. I propose that the presence of at least merely indicates that the prejacent is considered within a scale in which there are higher alternatives (which may or may not be true given what we know) and lower alternatives. I further argue that the different alternatives in the scale as well as the ordering relation need not be lexically generated but can be contextually provided. This is cashed out by making use of a discourse model.
"Only One At Least: Refining the Role of Discourse in Building Alternatives,"
University of Pennsylvania Working Papers in Linguistics: Vol. 19:
1, Article 3.
Available at: https://repository.upenn.edu/pwpl/vol19/iss1/3