How might the brain represent complex symbolic knowledge?

A novel category of theories is proposed, providing a potential explanation for the representation of complex knowledge in the human (and, more generally, mammalian) brain. Firstly, a "glocal" representation for concepts is suggested, involving localized representations in a sparse network of "concept neurons" in the Medial Temporal Lobe, coupled with a complex dynamical attractor representation in other parts of cortex. Secondly, it is hypothesized that a combi-natory logic like representation is used to encode abstract relationships without explicit use of variable bindings, perhaps using systematic asynchronization among concept neurons to indicate an analogue of the combinatory-logic operation of function application. While unraveling the specifics of the brain's knowledge representation mechanisms will require data beyond what is currently available, the approach presented here provides a class of possibilities that is neurally plausible and bridges the gap between neurophysiological realities and mathematical and computer science concepts.