Reactive inhibition

Reactive inhibition is a phrase coined by Clark L. Hull (1951) in his postulate X.A.:

Whenever a reaction R is evoked from an organism there is left an increment of primary negative drive I_R which inhibits to a degree according to its magnitude the reaction potential _SE_R to that response (Hull, 1951, p. 74).

According to Hull's postulate X.B. inhibition I dissipates exponentially with time t:.:

With the passage of time since its formation I_R spontaneously dissipates approximately as a simple decay function of the time t elapsed, i.e.,

Hull's decay formula is somewhat awkward and might give rise to confusion. For example, I'_R does not refer to the derivative of I_R. A more convenient way of writing the formula would be as follows:

with b = a ln ⁡ ( 10 ) . I ( 0 ) is the inhibition at the beginning the time interval [0,t]. Note, that if one takes the natural logarithm of both sides one obtains:

where Y ( t ) = ln ⁡ I ( t ) and Y ( 0 ) = ln ⁡ I ( 0 ) . The last formula is used in Inhibition Theory.