It is well known that a search engine can significantly benefit from an auxiliary database, which can suggest interpretations of the search query by means of the involved concepts and their interrelationship. The difficulty is to translate abstract notions like concept and interpretation into a concrete search algorithm that operates over the auxiliary database. To surpass existing heuristics, there is a need for a formal basis, which is realized in this paper through the framework of a search database system, where an interpretation is identified as a parse. It is shown that the parses of a query can be generated in polynomial time in the combined size of the input and the output, even if parses are restricted to those having a nonempty evaluation. Identifying that one parse is more specific than another is important for ranking answers, and this framework captures the precise semantics of being more specific; moreover, performing this comparison between parses is tractable. Las...