  What makes a presupposition of an utterance -- information taken for granted
by its speaker -- different from other pragmatic inferences such as an
entailment is projectivity (e.g., the negative sentence the boy did not stop
shedding tears presupposes the boy had shed tears before). The projectivity may
vary depending on the combination of presupposition triggers and environments.
However, prior natural language understanding studies fail to take it into
account as they either use no human baseline or include only negation as an
entailment-canceling environment to evaluate models' performance. The current
study attempts to reconcile these issues. We introduce a new dataset,
projectivity of presupposition (PROPRES, which includes 12k premise-hypothesis
pairs crossing six triggers involving some lexical variety with five
environments. Our human evaluation reveals that humans exhibit variable
projectivity in some cases. However, the model evaluation shows that the
best-performed model, DeBERTa, does not fully capture it. Our findings suggest
that probing studies on pragmatic inferences should take extra care of the
human judgment variability and the combination of linguistic items.
