  We propose TRACIE, a novel temporal reasoning dataset that evaluates the
degree to which systems understand implicit events -- events that are not
mentioned explicitly in natural language text but can be inferred from it. This
introduces a new challenge in temporal reasoning research, where prior work has
focused on explicitly mentioned events. Human readers can infer implicit events
via commonsense reasoning, resulting in a more comprehensive understanding of
the situation and, consequently, better reasoning about time. We find, however,
that state-of-the-art models struggle when predicting temporal relationships
between implicit and explicit events. To address this, we propose a
neuro-symbolic temporal reasoning model, SYMTIME, which exploits distant
supervision signals from large-scale text and uses temporal rules to combine
start times and durations to infer end times. SYMTIME outperforms strong
baseline systems on TRACIE by 5%, and by 11% in a zero prior knowledge training
setting. Our approach also generalizes to other temporal reasoning tasks, as
evidenced by a gain of 1%-9% on MATRES, an explicit event benchmark.
