Cognitive processes are often attributed to statistical or symbolic general-purpose mechanisms. Here we show that some spontaneous generalizations are driven by specialized, highly constrained symbolic operations. We explore how two types of artificial grammars are acquired, one based on repetitions and the other on characteristic relations between tones ("ordinal" grammars). Whereas participants readily acquire repetition-based grammars, displaying early electrophysiological responses to grammar violations, they perform poorly with ordinal grammars, displaying no such electrophysiological responses. This outcome is problematic for both general symbolic and statistical models, which predict that both types of grammars should be processed equally easily. This suggests that some simple grammars are acquired using "perceptual primitives" rather than general-purpose mechanisms; such primitives may be elements of a "toolbox" of specialized computational heuristics, which may ultimately allow constructing a psychological theory of symbol manipulation.