  In partially observed environments, it can be useful for a human to provide
the robot with declarative information that represents probabilistic relational
constraints on properties of objects in the world, augmenting the robot's
sensory observations. For instance, a robot tasked with a search-and-rescue
mission may be informed by the human that two victims are probably in the same
room. An important question arises: how should we represent the robot's
internal knowledge so that this information is correctly processed and combined
with raw sensory information? In this paper, we provide an efficient belief
state representation that dynamically selects an appropriate factoring,
combining aspects of the belief when they are correlated through information
and separating them when they are not. This strategy works in open domains, in
which the set of possible objects is not known in advance, and provides
significant improvements in inference time over a static factoring, leading to
more efficient planning for complex partially observed tasks. We validate our
approach experimentally in two open-domain planning problems: a 2D discrete
gridworld task and a 3D continuous cooking task. A supplementary video can be
found at http://tinyurl.com/chitnis-iros-18.
