A neurocomputational framework is described for characterizing how intuitive and deliberate processing are accomplished in the human brain. The framework is derived from memory systems theory and supported by research findings on contrasts between implicit versus explicit (nonconscious versus conscious) memory. Implicit intuition and deliberate deduction depend on separate types of memory supported by distinct brain networks. For optimal decision making, training should be designed to accommodate the operating characteristics of both types of memory. Furthermore, reliance on explicit memory can inhibit the use of implicit intuition, so training must facilitate effective interactions between the two types of mechanism. To aid investigations of these effects, we introduce a Mixture-of-Experts model that characterizes the interaction between memory systems - the PINNACLE model (Parallel Interacting Neural Networks Competing in Learning). This model captures the separate neural networks that reflect implicit and explicit processing, as well as their interaction, and it can thus guide the development of training approaches to maximize the benefits of concurrent use of both intuition and deliberation in decision making.