Information flow framed in a computational and complexity context is relevant to the understanding of cognitive processes and awareness. In this presentation, we begin with analyzing an information theory framework developed in recent years under Information and Integration Theory (IIT) based on interactions among partitions of cognitive information sets by Nobel Prize Laureate Gerald M. Edelman and by Giulio Tononi. We discuss the scope and limitations of these ideas, introducing a related measure for partitioning information sets. We introduce a set of postulates describing cognition as a partially ordered set of events in space and time. We consider the relevant sequential and concurrent computational concepts in an idealized minimal cognitive device. The concept of fundamental cognitive chain formalizes temporal limits of cognition.