 One very prominent class of non-logicist formalism does make an explicit nod in the direction of the brain: viz., artificial neural networks (or as they are often simply called, neural networks, or even just neural nets). (The structure of neural networks and more recent developments are discussed  above).  Because Minsky and Pappert’s (1969) Perceptrons led many (including, specifically, many sponsors of AI research and development) to conclude that neural networks didn’t have sufficient information-processing power to model human cognition, the formalism was pretty much universally dropped from AI. However, Minsky and Pappert had only considered very limited neural networks. Connectionism, the view that intelligence consists not in symbolic processing, but rather non-symbolic processing at least somewhat like what we find in the brain (at least at the cellular level), approximated specifically by artificial neural networks, came roaring back in the early 1980s on the strength of more sophisticated forms of such networks, and soon the situation was (to use a metaphor introduced by John McCarthy) that of two horses in a race toward building truly intelligent agents.