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Cognitive radio offers the promise of intelligent radios that can learn from and adapt to their environment. To date, most cognitive radio research has focused on policy-based radios that are hard-coded with a list of rules on how the radio should behave in certain scenarios. Some work has been done on radios with learning engines tailored for very specific applications. This article describes a concrete model for a generic cognitive radio to utilize a learning engine. The goal is to incorporate the results of the learning engine into a predicate calculus-based reasoning engine so that radios can remember lessons learned in the past and act quickly in the future. We also investigate the differences between reasoning and learning, and the fundamentals of when a particular application requires learning, and when simple reasoning is sufficient. The basic architecture is consistent with cognitive engines seen in AI research. The focus of this article is not to propose new machine learning algorithms, but rather to formalize their application to cognitive radio and develop a framework from within which they can be useful. We describe how our generic cognitive engine can tackle problems such as capacity maximization and dynamic spectrum access.