Existing data mining approaches to complex systems anomaly detection use uni-variate and/or multi-variate statistical hypothesis testing to assign anomaly scores to data streams associated with system components. The former approach assumes statistical independence of individual components, while the latter assumes substantial global systemic correlation. As a compromise between these two epistemological extremes, we present a data-mining approach hybridizing existing statistical techniques with theorem-proving methods to create a novel algorithm for anomaly detection, diagnosis and control in complex systems. Our algorithm takes sensor inputs from physical sensors providing system subcomponent performance data and outputs (i) a global systemic risk indicator and (ii) possible diagnosis hypotheses. We present results on three different systems, and in comparison with current state-of-the-art fault detection algorithms to demonstrate the viability of our approach. We find that our algorithm proves robust towards increased data dimensionality in contrast with existing clustering-based fault detection methods and can also detect contextual faults that are undetectable using existing statistical techniques.