What is prefix monotonicity?
This publication provides a definition of prefix monotonicity: link

Definition:

"Prefix monotonicity reflects a basic property of communicating systems: assume we have
observed a finite sequence of output messages for a corresponding finite sequence of input
messages. Then if we observe additional input (thus the old input sequence is a prefix of the extended one) we may just observe additional output (thus the old output sequence is a prefix of the extended one). Prefix monotonicity provides a notion of causality between input and output. It reflects the stepwise consumption of input and production of output and guarantees the existence of least fixed points, which is mandatory for giving meaning to communication feedback loops."