  Human communication is based on a variety of inferences that we draw from
sentences, often going beyond what is literally said. While there is wide
agreement on the basic distinction between entailment, implicature, and
presupposition, the status of many inferences remains controversial. In this
paper, we focus on three inferences of plain and embedded disjunctions, and
compare them with regular scalar implicatures. We investigate this comparison
from the novel perspective of the predictions of state-of-the-art large
language models, using the same experimental paradigms as recent studies
investigating the same inferences with humans. The results of our best
performing models mostly align with those of humans, both in the large
differences we find between those inferences and implicatures, as well as in
fine-grained distinctions among different aspects of those inferences.
