Primary sensory cortices are traditionally regarded as stimulus analysers. However, studies of associative learning-induced plasticity in the primary auditory cortex (A1) indicate involvement in learning, memory and other cognitive processes. For example, the area of representation of a tone becomes larger for stronger auditory memories and the magnitude of area gain is proportional to the degree that a tone becomes behaviorally important. Here, we used extinction to investigate whether ‘behavioral importance’ specifically reflects a sound’s ability to predict reinforcement (reward or punishment) vs. to predict any significant change in the meaning of a sound. If the former, then extinction should reverse area gains as the signal no longer predicts reinforcement. Rats (n = 11) were trained to bar-press to a signal tone (5.0 kHz) for water-rewards, to induce signal-specific area gains in A1. After subsequent withdrawal of reward, A1 was mapped to determine representational areas. Signal-specific area gains, estimated from a previously established brain–behavior quantitative function, were reversed, supporting the ‘reinforcement prediction’ hypothesis. Area loss was specific to the signal tone vs. test tones, further indicating that withdrawal of reinforcement, rather than unreinforced tone presentation per se, was responsible for area loss. Importantly, the amount of area loss was correlated with the amount of extinction (r = 0.82, P < 0.01). These findings show that primary sensory cortical representation can encode behavioral importance as a signal’s value to predict reinforcement, and that the number of cells tuned to a stimulus can dictate its ability to command behavior.