Mathematical principles of reinforcement were developed in order to (1) account for the interaction of target responding and other behavior; (2) provide a simple graphical representation; (3) deal with measurement artifacts; and (4) permit a coherent transition from a statics to a dynamics of behavior. Rats and pigeons were trained to make a target response while general activity was measured with a stabilimeter, The course ofbehavioral change was represented as a trajectory through a two-dimensional behavior space, The trajectories rotated toward or away from the target dimension as the coupling between the target response and the incentive was varied. Higher rates of reinforcement expanded the trajectories; satiation and extinction contracted them. Concavity in some trajectories provided data for a dynamic generalization of the model. piing is our principle ofselection. This paper will analyze the effects on behavior when these two factors are independently manipulated.The first principle states that the delivery ofincentives increases the activity ofan organism. Killeen (1975) reported levels of general activity in pigeons under a wide range ofreinforcement rates. When corrected for ceilings on response rates, the activity levels were proportional to the rate of reinforcement (see Figure 1). Killeen, Hanson, and Osborne (1978) derived a model of incentive motivation that predicted the change in arousal levels as a function of changes in the rate of reinforcement. They fed pigeons once every day and measured the resulting activity, which averaged 360 responses/reinforcer. They showed that the activation cumulates according to an exponentially weighted moving average, whose output is the arousal level, A:where R is the rate ofreinforcement. Equation 1 predicted Killeen's (1975) data (Figure 1), with a = 360.Killeen (1998) extended the notion of arousal and its accumulation to other contexts, including classical and avoidance conditioning, in which the phenomena of pseudoconditioning and warm-up are its manifestations. The next step is to develop the theory, so as to deal generally with temporal constraints on responding.
Constraints on responding.Constraints are limitations-things organisms can't do no matter how powerful the motivation or how effective the conditioning. They are the complements ofpredispositions-things organisms do with seemingly little motivation or conditioning. Skinner (1938) represented this difference in sensitivities to reinforcement in his extinction ratio. Most generally, Seligman (1970) placed responses on a continuum of preparedness, ranging from contra-prepared through neutral to prepared. Here the focus is on temporal constraints-the increasing difficulty of making a response as a function of the ongoing rate of responding. The second principle can be succinctly stated: Responses compete for expression.Motivation, association, and response constraints are central phenomena in learning and performance. A recent