  This paper examines how an event from one random variable provides pointwise
mutual information about an event from another variable via probability mass
exclusions. We start by introducing probability mass diagrams, which provide a
visual representation of how a prior distribution is transformed to a posterior
distribution through exclusions. With the aid of these diagrams, we identify
two distinct types of probability mass exclusions---namely informative and
misinformative exclusions. Then, motivated by Fano's derivation of the
pointwise mutual information, we propose four postulates which aim to decompose
the pointwise mutual information into two separate informational components: a
non-negative term associated with the informative exclusion and a non-positive
term associated with the misinformative exclusions. This yields a novel
derivation of a familiar decomposition of the pointwise mutual information into
entropic components. We conclude by discussing the relevance of considering
information in terms of probability mass exclusions to the ongoing effort to
decompose multivariate information.
