Inhibition theory

Inhibition theory is based on the basic assumption that during the performance of any mental task requiring a minimum of mental effort, the subject actually goes through a series of alternating latent states of distraction (non-work 0) and attention (work 1) which cannot be observed and are completely imperceptible to the subject. T11, T01, T12, T02, T13, T03, ..., Inhibition theory is based on the basic assumption that during the performance of any mental task requiring a minimum of mental effort, the subject actually goes through a series of alternating latent states of distraction (non-work 0) and attention (work 1) which cannot be observed and are completely imperceptible to the subject. Additionally, the concept of inhibition or reactive inhibition which is also latent, is introduced. The assumption is made that during states of attention inhibition linearly increases with a slope a1 and during states of distraction inhibition linearly decreases with a slope a0.According to this view the distraction states can be considered a sort of recovery state. It is further assumed, that when the inhibition increases during a state of attention, depending on the amount of increase, the inclination to switch to a distraction state also increases. When inhibition decreases during a state of distraction, depending on the amount of decrease, the inclination to switch to an attention state increases. The inclination to switch from one state to the other is mathematically described as a transition rate or hazard rate, making the whole process of alternating distraction times and attention times a stochastic process. A non-negative continuous random variable T represents the time until an event will take place. The hazard rate λ(t) for that random variable is defined to be the limiting value of the probability that the event will occur in a small interval ; given the event has not occurred before time t, divided by Δt. Formally, the hazard rate is defined by the following limit: The hazard rate λ(t) can also be written in terms of the density function or probability density function f(t) and the distribution function or cumulative distribution function F(t): The transition rates λ1(t), from state 1 to state 0, and λ0(t), from state 0 to state 1, depend on inhibition Y(t): λ1(t) = ℓ1(Y(t)) and λ0(t) = ℓ0(Y(t)), where ℓ1 is a non-decreasing function and ℓ0 is a non-increasing function. Note, that ℓ1 and l0 are dependent on Y, whereas Y is dependent on T. Specification of the functions l1 and l0 leads to the various inhibition models. What can be observed in the test are the actual reaction times. A reaction time is the sum of a series of alternating distraction times and attention times, which cannot be observed. It is, nevertheless, possible to estimate from the observable reaction times some properties of the latent process of distraction times and attention times, i.e., the average distraction time, the average attention time, and the ratio a1/a0. In order to be able to simulate the consecutive reaction times, inhibition theory has been specified into various inhibition models. One is the so-called beta inhibition model. In the beta-inhibition model, it is assumed that the inhibition Y(t) oscillates between two boundaries which are 0 and M (M for Maximum), where M is positive. In this model ℓ1 and ℓ0 are as follows: