Four theoretical bases for detecting a contingency between behavior an
d consequent stimuli are considered: contiguity, correlation, conditio
nal probability, and logical implication. It is argued that conditiona
l probability analysis is statistically the most powerful of these opt
ions, in part due to its provision of two indices of contingency: a fo
rward time probability that reinforcement follows behavior and a backw
ard time probability that behavior precedes reinforcement. Evidence is
cited that both indices appear to bear on the learning of a variety o
f animals, although they are unequally salient to human adults and to
artificial neural networks designed to solve time-series functions. It
is hypothesized that humans may acquire the capacity to detect contin
gency in the progressive sequence: contiguity, correlation, forward ti
me conditional probability, backward time conditional probability, and
ultimately logical implication.