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In this paper we investigate the use of classical logic as a basis for instantiating abstract argumentation frameworks. In the first part, we propose desirable properties of attack relations in the form of postulates and classify several well-known attack relations from the literature with regards to the satisfaction of these postulates. Furthermore, we provide additional postulates that help us prove characterisation results for these attack relations. In the second part of the paper, we present postulates regarding the logical content of extensions of argument graphs that may be constructed with classical logic. We then conduct a comprehensive study of the status of these postulates in the context of the various combinations of attack relations and extension semantics.