Dynamical logic observers for finite automata

A state estimation problem is formulated for a partially observed input-state-output (I-S-O) automaton, and the concept of a dynamical (default) logic observer is introduced. The state estimation problem is posed in terms of (i) the problem of constructing a classical dynamical system (CDS) which generates a sequence of state estimates, and (ii) the problem of the construction of a dynamical logic system (DLS) which generates a sequence of propositions that correctly describe properties of the state of the automaton. A simple illustrative example is presented in which a classical dynamical observer and a dynamical logic observer are constructed to solve the observation problem for a partially observed automaton