  Lifted probabilistic inference (Poole, 2003) and symbolic dynamic programming
for lifted stochastic planning (Boutilier et al, 2001) were introduced around
the same time as algorithmic efforts to use abstraction in stochastic systems.
Over the years, these ideas evolved into two distinct lines of research, each
supported by a rich literature. Lifted probabilistic inference focused on
efficient arithmetic operations on template-based graphical models under a
finite domain assumption while symbolic dynamic programming focused on
supporting sequential decision-making in rich quantified logical action models
and on open domain reasoning. Given their common motivation but different focal
points, both lines of research have yielded highly complementary innovations.
In this chapter, we aim to help close the gap between these two research areas
by providing an overview of lifted stochastic planning from the perspective of
probabilistic inference, showing strong connections to other chapters in this
book. This also allows us to define Generalized Lifted Inference as a paradigm
that unifies these areas and elucidates open problems for future research that
can benefit both lifted inference and stochastic planning.
