  The unification of logic and probability is a long-standing concern in AI,
and more generally, in the philosophy of science. In essence, logic provides an
easy way to specify properties that must hold in every possible world, and
probability allows us to further quantify the weight and ratio of the worlds
that must satisfy a property. To that end, numerous developments have been
undertaken, culminating in proposals such as probabilistic relational models.
While this progress has been notable, a general-purpose first-order knowledge
representation language to reason about probabilities and dynamics, including
in continuous settings, is still to emerge. In this paper, we survey recent
results pertaining to the integration of logic, probability and actions in the
situation calculus, which is arguably one of the oldest and most well-known
formalisms. We then explore reduction theorems and programming interfaces for
the language. These results are motivated in the context of cognitive robotics
(as envisioned by Reiter and his colleagues) for the sake of concreteness.
Overall, the advantage of proving results for such a general language is that
it becomes possible to adapt them to any special-purpose fragment, including
but not limited to popular probabilistic relational models.
