  Contextual commonsense inference is the task of generating various types of
explanations around the events in a dyadic dialogue, including cause,
motivation, emotional reaction, and others. Producing a coherent and
non-trivial explanation requires awareness of the dialogue's structure and of
how an event is grounded in the context. In this work, we create CICEROv2, a
dataset consisting of 8,351 instances from 2,379 dialogues, containing multiple
human-written answers for each contextual commonsense inference question,
representing a type of explanation on cause, subsequent event, motivation, and
emotional reaction. We show that the inferences in CICEROv2 are more
semantically diverse than other contextual commonsense inference datasets. To
solve the inference task, we propose a collection of pre-training objectives,
including concept denoising and utterance sorting to prepare a pre-trained
model for the downstream contextual commonsense inference task. Our results
show that the proposed pre-training objectives are effective at adapting the
pre-trained T5-Large model for the contextual commonsense inference task.
