Mathematical models of classical conditioning : a critical review and extensions

The history of classical conditioning is summarized. The contributions and weaknesses of several earlier models of classical conditioning are studied. Two new neuronal models are proposed. The first, called the delay-producing connections (or DPC) model, is an extension of the Klopf (1988) and Sutton & Barto (1981) models. The DPC model makes two contributions: (1) it represents the trace of each conditioned stimuli (CS) by differential equations; and (2) it replaces each CS in the activation rule with a trace of the relevant CS. A method is suggested to measure the trace of a CS. The second model, called the adaptive delays (or AD) model, is proposed as an extension of the DPC model to account for the phenomenon of inhibition of delay. Both models reproduce the shape of a CR, the curve of efficacy of conditioning as a function of the interstimulus interval (ISI), the dependence of the optimal ISI on CS duration, the extinction of a CR (even for long lasting CSs as opposed to Klopf's (1988) model), and several other properties of classical conditioning