  Modelling is an essential procedure in analyzing and controlling a given
logical dynamic system (LDS). It has been proved that deterministic LDS can be
modeled as a linear-like system using algebraic state space representation.
However, due to the inherently non-linear, it is difficult to obtain the
algebraic expression of a stochastic LDS. This paper provides a unified
framework for transition analysis of LDSs with deterministic and stochastic
dynamics. First, modelling of LDS with deterministic dynamics is reviewed. Then
modeling of LDS with stochastic dynamics is considered, and non-equivalence
between subsystems and global system is proposed. Next, the reason for the
non-equivalence is provided. Finally, consistency condition is presented for
independent model and conditional independent model.
