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Conceptual graphs (CGs) are a knowledge representation formalism that models monotonic first-order logic. However, in the case of an active knowledge base and in other cases, it is necessary to modify a CG dynamically, rendering the preceding static first-order CG possibly inconsistent and in need of further analysis. In order to extend monotonic first-order logic to non-monotonic second-order computation, and therefore achieve all of the power of a modern computer, CGs need to use atomic actors to represent change. To illustrate the power of actors, we represent the well-defined Turing machine; this has the added effect of showing that CGs can represent any of the power of a modern computer. This addition to the CG theory will have other similar practical effects. [ABSTRACT FROM AUTHOR]