  The paper extends Bayesian networks (BNs) by a mechanism for dynamic changes
to the probability distributions represented by BNs. One application scenario
is the process of knowledge acquisition of an observer interacting with a
system. In particular, the paper considers condition/event nets where the
observer's knowledge about the current marking is a probability distribution
over markings. The observer can interact with the net to deduce information
about the marking by requesting certain transitions to fire and observing their
success or failure.
  Aiming for an efficient implementation of dynamic changes to probability
distributions of BNs, we consider a modular form of networks that form the
arrows of a free PROP with a commutative comonoid structure, also known as term
graphs. The algebraic structure of such PROPs supplies us with a compositional
semantics that functorially maps BNs to their underlying probability
distribution and, in particular, it provides a convenient means to describe
structural updates of networks.
