  Superlatives are used to single out elements with a maximal/minimal property.
Semantically, superlatives perform a set comparison: something (or some things)
has the min/max property out of a set. As such, superlatives provide an ideal
phenomenon for studying implicit phenomena and discourse restrictions. While
this comparison set is often not explicitly defined, its (implicit)
restrictions can be inferred from the discourse context the expression appears
in. In this work we provide an extensive computational study on the semantics
of superlatives. We propose a unified account of superlative semantics which
allows us to derive a broad-coverage annotation schema. Using this unified
schema we annotated a multi-domain dataset of superlatives and their semantic
interpretations. We specifically focus on interpreting implicit or ambiguous
superlative expressions, by analyzing how the discourse context restricts the
set of interpretations. In a set of experiments we then analyze how well models
perform at variations of predicting superlative semantics, with and without
context. We show that the fine-grained semantics of superlatives in context can
be challenging for contemporary models, including GPT-4.
