A new inductive learning system, LAB (Learning for ABduction), is presented which acquires abductive rules from a set of training examples. The goal is to find a small knowledge base which, when used abductively, diagnoses the training examples correctly and generalizes well to unseen examples. This contrasts with past systems that inductively learn rules that are used deductively. Each training example is associated with potentially multiple categories (disorders), instead of one as with typical learning systems. LAB uses a simple hill-climbing algorithm to efficiently build a rule base for a set-covering abductive system. LAB has been experimentally evaluated and compared to other learning systems and an expert knowledge base in the domain of diagnosing brain damage due to stroke.