Model Checking Sum and Product

We model the well-known Sum-and-Product problem in a modal logic, and verify its solution in a model checker. The modal logic is public announcement logic. This logic contains operators for knowledge, but also for the informational consequences of public announcements. The logic is interpreted on multi-agent Kripke models. The information in the riddle can be represented in the traditional way by number pairs, so that Sum knows their sum and Product their product, but also as an interpreted system, so that Sum and Product at least know their local state. We show that the different representations are isomorphic. The riddle is then implemented and its solution verified in the epistemic model checker DEMO. This can be done, we think, surprisingly elegantly. It involves reformulations to facilitate the computation.