  The concept of updating (or conditioning or revising) a probability
distribution is fundamental in (machine) learning and in predictive coding
theory. The two main approaches for doing so are called Pearl's rule and
Jeffrey's rule. Here we make, for the first time, mathematically precise what
distinguishes them: Pearl's rule increases validity (expected value) and
Jeffrey's rule decreases (Kullback-Leibler) divergence. This forms an instance
of a more general distinction between learning from what's right and learning
from what's wrong. The difference between these two approaches is illustrated
in a mock cognitive scenario.
