Fault diagnosis is becoming increasingly important and difficult with the growing pervasiveness and complexity of computer systems. We propose in this paper a general semantic framework for fault ascription, a precise form of fault diagnosis that relies on counterfactual analysis for identifying necessary and sufficient causes of faults in component-based systems. Our framework relies on configuration structures to handle concurrent systems, partial and distributed observations in a uniform way. It defines basic conditions for a counterfactual analysis of necessary and sufficient causes, and it presents a refined analysis that conforms to our basic conditions while avoiding various infelicities.