Quantum-like behavior without quantum physics III : Logic and memory

We employ some of the machinery developed in previous work to investigate the inferential and memory functions of quantum-like neural networks. We set up a logical apparatus to implement this in the form of a Gentzen sequent calculus which codifies some of the combinatory rules for the state spaces of the neuronal networks introduced earlier. We discuss memory storage in this context and along the way find formal proof that synchronicity promotes binding and storage. These results lead to an algorithmic fragment in calculus that simulates the memory function known as pattern completion. This claim is tested by noting that the failure of certain steps in the algorithm leads to memory deficits essentially identical to those found in such pathologies as Alzheimer's dementia, schizophrenia, and certain forms of autism. Moreover, a specific "power-of-two" wiring architecture and computational logic, which have been postulated and observed across many brain circuits, emerge spontaneously from our model. We draw conclusions concerning the possible nature of such mental processes qua computations.