Classical logic based argumentation (ClAr) characterises single agent non-monotonic reasoning and enables distributed non-monotonic reasoning amongst agents in dialogues. However, features of ClAr that have been shown sufficient to ensure satisfaction of rationality postulates, preclude their use by resource bounded agents reasoning individually, or dialectically in real-world dialogue. This paper provides a new formalisation of ClAr that is both suitable for such uses and satisfies the rationality postulates. We illustrate by providing a rational dialectical characterisation of Brewka's non-monotonic Preferred Subtheories defined under the assumption of restricted inferential capabilities.