  Recent work has unveiled a theory for reasoning about the decisions made by
binary classifiers: a classifier describes a Boolean function, and the reasons
behind an instance being classified as positive are the prime-implicants of the
function that are satisfied by the instance. One drawback of these works is
that they do not explicitly treat scenarios where the underlying data is known
to be constrained, e.g., certain combinations of features may not exist, may
not be observable, or may be required to be disregarded. We propose a more
general theory, also based on prime-implicants, tailored to taking constraints
into account. The main idea is to view classifiers in the presence of
constraints as describing partial Boolean functions, i.e., that are undefined
on instances that do not satisfy the constraints. We prove that this simple
idea results in reasons that are no less (and sometimes more) succinct. That
is, not taking constraints into account (e.g., ignored, or taken as negative
instances) results in reasons that are subsumed by reasons that do take
constraints into account. We illustrate this improved parsimony on synthetic
classifiers and classifiers learned from real data.
