We propose a primitive called PJOIN, for "predictive join," which combines and extends the operations JOIN and LINK, which Valiant proposed as the basis of a computational theory of cortex. We show that PJOIN can be implemented in Valiant's model. We also show that, using PJOIN, certain reasonably complex learning and pattern matching tasks can be performed, in a way that involves phenomena which have been observed in cognition and the brain, namely memory-based prediction and downward traffic in the cortical hierarchy.