@misc{cogprints591, volume = {17}, number = {1}, author = {Peter Killeen}, title = {Mathematical Principles of Reinforcement: Based on the Correlation of Behaviour with Incentives in Short-Term Memory}, publisher = {Cambridge University Press}, journal = {Behavioral and Brain Sciences}, pages = {105--172}, year = {1994}, keywords = {reinforcement, memory, coupling, contingency, contiguity, tuning curves, activation, schedules, trajectories, response rate}, url = {http://cogprints.org/591/}, abstract = {Effective conditioning requires a correlation between the experimenter's definition of a response and an organism's, but an animal's perception of its behavior differs from ours. Various definitions of the response are explored experimentally using the slopes of learning curves to infer which comes closest to the organism's definition. The resulting exponentially weighted moving average provides a model of memory which grounds a quantitative theory of reinforcement in which incentives excite behavior and focus the excitement on the responses present in memory at the same time. The correlation between the organism's memory and the behavior measured by the experimenter is given by coupling coefficients derived for various schedules of reinforcement. For simple schedules these coefficients can be concatenated to predict the effects of complex schedules and can be inserted into a generic model of arousal and temporal constraint to predict response rates under any scheduling arrangement. According to the theory, the decay of memory is response-indexed rather than time-indexed. Incentives displace memory for the responses that occur before them and may truncate the representation of the response that brings them about. This contiguity-weighted correlation model bridges opposing views of the reinforcement process and can be extended in a straightforward way to the classical conditioning of stimuli. Placing the short-term memory of behavior in so central a role provides a behavioral account of a key cognitive process.} }