This article provides the foundation for a new predictive theory of animal learning that is based upon a simple logical model. The knowledge of experimental subjects at a given time is described using logical equations. These logical equations are then used to predict a subject’s response when presented with a known or a previously unknown situation. This new theory suc- cessfully anticipates phenomena that existing theories predict, as well as phenomena that they cannot. It provides a theoretical account for phenomena that are beyond the domain of existing models, such as extinction and the detection of novelty, from which “external inhibition” can be explained. Examples of the methods applied to make predictions are given using previously published results. The present theory proposes a new way to envision the minimal functions of the nervous system, and provides possible new insights into the way that brains ultimately create and use knowledge about the world.