Researchers using epistemic logic as a formal framework for studying knowledge properties of AI systems often interpret the knowledge formula K(z, ~) to mean that machine x encodes ~ in its state as a syntactic formula or can derive it inferentially. By defining K(x, ~), instead, in terms of the correlation between the state of the machine and that of its environment, the formal properties of modal system S5 can be satisfied without having to store representations of formulas as data structures. In this paper, we apply the correlational definition of knowledge to machines with composite structure. In particular, we describe how epistemic properties of synchronous digital machines can be analyzed, starting at the level of gates and delays, by modeling the machine's components as agents in a multi-agent system and reasoning about the flow of information among them. We also introduce Rex, a language for recursively computing machine descriptions, and illustrate how it can be used to construct machines with provable knowledge properties.

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