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