  Within Dialogue Modeling research in AI and NLP, considerable attention has
been spent on ``dialogue state tracking'' (DST), which is the ability to update
the representations of the speaker's needs at each turn in the dialogue by
taking into account the past dialogue moves and history. Less studied but just
as important to dialogue modeling, however, is ``common ground tracking''
(CGT), which identifies the shared belief space held by all of the participants
in a task-oriented dialogue: the task-relevant propositions all participants
accept as true. In this paper we present a method for automatically identifying
the current set of shared beliefs and ``questions under discussion'' (QUDs) of
a group with a shared goal. We annotate a dataset of multimodal interactions in
a shared physical space with speech transcriptions, prosodic features,
gestures, actions, and facets of collaboration, and operationalize these
features for use in a deep neural model to predict moves toward construction of
common ground. Model outputs cascade into a set of formal closure rules derived
from situated evidence and belief axioms and update operations. We empirically
assess the contribution of each feature type toward successful construction of
common ground relative to ground truth, establishing a benchmark in this novel,
challenging task.
