In this paper, we generalize our formal approach to modelling PRS agents away from PRS-specific assumptions to more general theories of rationality, while not losing the concreteness of the connection between an agent's mental states and formal models, using three "puzzles" in the logic of intention to motivate our extended approach. We show how the theory can be used to represent solutions to the puzzles and draw out insights into how agent architectures may be extended to handle these more complex scenarios.