Hybrid connectionist symbolic systems have been the subject of much recent research in AI. By focusing on the implementation of high-level human cognitive processes (e.g., rule-based inference) on low-level, brain-like structures (e.g., neural networks), hybrid systems inherit both the efficiency of connectionism and the comprehensibility of symbolism. This paper presents the Basic Reasoning Applicator Implemented as a Neural Network (BRAINN). Inspired by the columnar organisation of the human neocortex, BRAINN's architecture consists of a large hexagonal network of Hopfield nets, which encodes and processes knowledge from both rules and relations. BRAINN supports both rule-based reasoning and similarity-based reasoning. Empirical results demonstrate promise.