Many AI systems have a black box nature that makes it difficult to understand how they make their recommendations. This can be unsettling, as the designer cannot be certain how the system will respond to novelty. To penetrate our Naïve Bayes recommender's black box, we first asked, what do we want to know from our system, and how can it be obtained? The answers led us to recursively define a common lexicon with the AI, a lingua franca, using the very items that the system ranks to create meta-symbols recognized by the system, and enabling us to understand the system's knowledge in plain terms and at different levels of abstraction. As one bonus, using its existing knowledge, the lingua franca can enable the system to extend recommendations to related, but entirely new areas, ameliorating the cold start problem. We also supplement the lingua franca with techniques for visualizing the system's knowledge state, develop metrics for evaluating the meaningfulness of terms in the lingua franca, and generalize the requirements for developing a similar lingua franca in other applications.