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We develop a general framework for abstracting online behavior of an agent that may acquire new knowledge during execution (e.g., by sensing), in the situation calculus and ConGolog. We assume that we have both a high-level action theory and a low-level one that represent the agent's behavior at different levels of detail. In this setting, we define ability to perform a task/achieve a goal, and then show that under some reasonable assumptions, if the agent has a strategy by which she is able to achieve a goal at the high level, then we can refine it into a low-level strategy to do so.