Modified Numerals
Overview
Modified numerals are expressions like at least n and more than n. It is often assumed that superlatives modifiers give rise to ignorance inferences, while comparative modifiers do not.
John has at least four children.
John has more than three children.
While (1) gives rise to an ignorance inference (the speaker does not know how many children John has), the same inference is more difficult to get in the case of (2). This is surprising, since these expression are considered equivalent in traditional accounts of quantified expressions (e.g. generalized quantifiers).
In this class, we will then present a first-order version of the BSML system presented in the previous class (Aloni & van Ormondt 2021) and analyze how this account deals with cases like (1) and (2).