The problem of the construction of a Logic Observer,
which generates a sequence of propositions that correctly describe
 system state properties, is mainly intended to solve the state
estimate of finite state machines. 
Of particular interest is the convergence of the logic-based dynamical
system statements (in an appropriate sense) to true
characterizations of the system state.
This paper demonstrates that this observer can be built within
a logic-based framework. It starts
with an informal discussion of the nature of logic -- focusing on
the predicate calculus -- and discusses the fundamental concepts
associated with these formal systems. Later in the paper, the
formal definition of the concepts of the logic-based dynamical
observer is presented. An arbitrary automaton is selected
as an example to understand the simulation and the expert
system presented to accomplish the task.
In this paper, the assumption is that the automata representation in
state space systems is expressed by  the quintuple set of
states, set of inputs, set of outputs, transition functions and 
output functions. An automaton is taken as a deterministic
input-state-output (finite) system.