Non-existence of Upper Bound to Inferencing Level in Decentralized Discrete Event Control

In the authors' earlier work, the notion of inference-observability was introduced to characterize the existence of decentralized supervisors that perform multi-level inferencing against self-ambiguity and ambiguities of the others to jointly arrive at a correct control decision. When the property of $N$ -inference-observability holds, $N$ -levels of inferencing is needed. We show in this paper that the class of $N$ -inference-observable languages increases strictly monotonically as the parameter $N$ is increased. We further show that in general there does not exist an upper bound on the number of levels of inferencing required.