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

Sufficient reasons for classifier decisions in the presence of constraints