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On knowledge-based programming with sensing in the situation calculus

We consider a class of knowledge-based Golog programs with sense actions. These programs refer explicitly to an agent's knowledge, and are designed to execute on-line, and under a dynamic closed-world assumption on knowledge. On-line execution of sense actions dynamically updates the background axioms with sentences asserting knowledge of the sense actions' outcomes. We formalize what all this might mean, and show that under suitable assumptions the knowledge modality in such programs can be implemented by provability. This leads to an on-line Golog interpreter for such programs, which we demonstrate on a knowledge-based program with sensing for the blocks world.