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System security continues to be of increasing importance. To effectively address both natural and intentional threats to large systems, the threats must be cataloged and analyzed. Extremely large and complex systems can have an accordingly large number of threat scenarios. Simply listing the threats and devising countermeasures for each is ineffective and not efficient. We describe a threat cataloging methodology whereby a large number of threats can be efficiently cataloged and analyzed for common features. This allows countermeasures to be formulated that address a large number of threats that share common features. The methodology utilizes Multiple-Valued Logic for describing the state of a large system and a multiple-valued decision diagram (MDD) for the threat catalog and analysis.