This paper proposes a logical framework for studying the structure of moral responsibility for outcomes. The analysis incorporates two vital features: an agency condition and a negative condition of an alternative possibility. The logical language allows us to identify and disambiguate seven plausible criteria for moral responsibility. To accommodate interdependent decision contexts, the semantics are given in terms of so-called responsibility games. The logical framework enables us to classify the logical relations between these seven criteria for moral responsibility. Although all (...) seven criteria are logically distinct, I also identify circumstances where the seven criteria locally reduce to only three. (shrink)