# 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 IR which inhibits to a degree according to its magnitude the reaction potential SER 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 IR spontaneously dissipates approximately as a simple decay function of the time t elapsed, i.e.,

${\displaystyle I'_{R}=I_{R}x10^{-at}}$ (Hull, 1951, p. 74).

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

${\displaystyle I(t)=I(0)e^{-bt}}$

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

${\displaystyle Y(t)=Y(0)-bt}$

where ${\displaystyle Y(t)=\ln I(t)}$ and ${\displaystyle Y(0)=\ln I(0)}$. The last formula is used in inhibition theory.

## References

• Hull, C.L.: Essentials of behavior. Westport (Connecticut): Greenwood Press, 1951.