According to the law of association by contiguity the learning of associations can be described as follows: If two words i and j occur together, the association strength between i and j is increased by a constant fraction of the difference between the maximum and the actual association strength. This leads for association strengths between 0 and 1 to the following formula:
If word i occurs in another context, i. e. not in proximity to word j, the association strength between i and j is decreased by a constant fraction:
Under the assumption that the learning rate and the inhibition rate are of identical size, the expected value of the association strength from i to j for is equal to the conditional probability of j given i (compare Foppa, 1965):
From these assumptions it could be expected that a stimulus word i leads to those response j, for which the value of equation 3 is at a maximum.
Rapp & Wettler (1991) compared this with other predictions, where additional assumptions on learning and reproduction were taken into account. With equation 3, mainly words with high corpus frequencies, e. g. function words, were predicted as associative responses. The predictions were improved when the following formula was used with an exponent of , and the word with the highest was considered to be the associative response.
The introduction of the denominator indicates that in the association experiment less frequent words are used than during language production. This inhibition of frequent words can be explained by the experimental situation, which furthers responses that are specific to the stimulus word. The exponential function can be interpreted as the tendency that subjective estimations are often found to be exponential functions of the quantities to be estimated.