A methodology for nonmarket goods is presented based on preference algebra and set theory that allows us to specify exactly when preference assumptions such as weak complementarity can be tested against revealed preference information. Revealed preference is insufficient for welfare analysis involving state preference variables such as nonmarket goods. The preference and set-theoretic structure presented here is specifically designed to characterize the minimal additional preference information necessary for exact welfare analysis, and also provides a common basis for specifying the many context-specific methods that have been proposed for closing the information gap (whether or not they provide this minimal information). The paper closes with examples demonstrating how this structure can be used as a methodology for working with assumptions about preference structure, focusing on when such assumptions can be tested against revealed preference. This includes an extended examination of weak complementarity and related issues, followed by five shorter examples including two types of repackaging for price indices and the new and disappearing goods problem.