Relational memory, the ability to make and remember associations between objects, is an essential component of mammalian reasoning. In relational memory tasks, it has been shown that periods of offline processing, such as sleep, are critical to making indirect associations. To understand biophysical mechanisms behind the role of sleep in improving relational memory, we developed a model of the thalamocortical network to test how slow-wave sleep affects performance on an unordered relational memory task. First, the model was trained in the awake state on a paired associate inference task, in which the model learned to recall direct associations. After a period of subsequent slow-wave sleep, the model developed the ability to recall indirect associations. We found that replay, during sleep, of memory patterns learned in awake increased synaptic connectivity between neurons representing the item that was overlapping between tasks and neurons representing the unlinked items of the different tasks; this forms a...