  We present a model for exact recursive Bayesian filtering based on lifted
multiset states. Combining multisets with lifting makes it possible to
simultaneously exploit multiple strategies for reducing inference complexity
when compared to list-based grounded state representations. The core idea is to
borrow the concept of Maximally Parallel Multiset Rewriting Systems and to
enhance it by concepts from Rao-Blackwellization and Lifted Inference, giving a
representation of state distributions that enables efficient inference. In
worlds where the random variables that define the system state are exchangeable
-- where the identity of entities does not matter -- it automatically uses a
representation that abstracts from ordering (achieving an exponential reduction
in complexity) -- and it automatically adapts when observations or system
dynamics destroy exchangeability by breaking symmetry.
