We propose a framework for reasoning from inconsistent knowledge bases using minimal hitting sets, i. e., sets of interpretations such that each formula of the knowledge base is satisfied by at least one those interpretations. By additionally considering preference orders over minimal hitting sets, we can define a wide variety of non-monotonic inference relations. We consider concrete preference orders based on set inclusion, cardinality, the number of conflicting atoms within the hitting set, and using the Hamming distance between pairs of interpretations. We compare the resulting inference relations, characterize their logical properties, and position them relative to classical inference from maximal consistent subsets. Finally, we show that inference based on minimal conflicting atoms coincides with reasoning in Priest’s 3-valued logic.