A fundamental problem, faced by children and scientists alike, is to discern causal structure of the world from very limited experience. The goal of this talk will be to show how the problem of causal inference can be usefully and precisely understood as a logical problem. The logical perspective allows formulating and answering questions about how difficult it is to reach causal conclusions from alternative sources of data. In particular, it allows assessing the empirical status of assumptions sufficient to bridge the logical gap between limited data and substantive causal conclusions. The focus of the talk will be on how these various concepts can be codified, what the results say and what they might tell us about causal-inductive inquiry.