On the mathematical formalization of the Inhibited Elements Model

The Inhibited Elements Model (Brandon et al., 2000; Wagner and Brandon, 2000) has been proposed as an elemental model that may reproduce the configural model proposed by Pearce (1987, 1994), and although its mathematical formalization has been recently improved by Thorwart and Lachnit (2020), whether it actually reproduces Pearce’s model has remained an open question. In this work I further develop the mathematical formalization of the Inhibited Elements Model by casting it within the formalism proposed by Ghirlanda (2015, 2018). In doing so I will derive the conditions under which the Inhibited Elements Model reproduces Pearce’s model, showing that when all stimuli are assumed of the same “salience” these models coincide only when the application is restricted to compounds that either contain each other or have no common elements. Finally, the mathematical formalization developed here will be applied to the analytic comparison of the Inhibited Elements Model, Rescorla and Wagner’s model (Rescorla and Wagner, 1972; Wagner and Rescorla, 1972), and Pearce’s model in the context of several learning phenomena.