A NEW UNDERSTANDING OF THE FOUNDATION OF LINEAR-SYSTEM ANALYSIS AND AN EXTENSION TO NONLINEAR CASES

Linear system analysis has been used to generate a mathematical descri ption of how reinforcement regulates free operant behavior. The centra l assumption of the analysis is that the relationship between an organ ism's behavior and a schedule of reinforcement can be described by a l inear differential equation. In this article, the linear differential equation assumption is shown to be equivalent to asserting that curren t behavior is determined by past reinforcement events. that is, by a h istory of reinforcement. In addition to clarifying the theory and impr oving its face validity, this new understanding of the theory's founda tion suggests a way of describing nonlinear phenomena. The extension t o nonlinear cases consists of a series, the terms of which describe in creasingly complex interactions among reinforcers. The series is very general and can be used to develop specific models of considerable com plexity about how reinforcement regulates behavior.