MPR.

Mathematical Principles of Reinforcement (MPR) is a theory of reinforcement schedules. This paper reviews the origin of the principles constituting MPR: arousal, association and constraint. Incentives invigorate responses, in particular those preceding and predicting the incentive. The process that generates an associative bond between stimuli, responses and incentives is called coupling. The combination of arousal and coupling constitutes reinforcement. Models of coupling play a central role in the evolution of the theory. The time required to respond constrains the maximum response rates, and generates a hyperbolic relation between rate of responding and rate of reinforcement. Models of control by ratio schedules are developed to illustrate the interaction of the principles. Correlations among parameters are incorporated into the structure of the models, and assumptions that were made in the original theory are refined in light of current data.