A probabilistic learning model for vague queries and missing or imprecise information in databases is described. Instead of retrieving only a set of answers, our approach yields a ranking of objects from the database in response to a query. By using relevance judgements from the user about the objects retrieved, the ranking for the actual query as well as the overall retrieval quality of the system can be further improved. For specifying different kinds of conditions in vague queries, the notion of vague predicates is introduced. Based on the underlying probabilistic model, also imprecise or missing attribute values can be treated easily. In addition, the corresponding formulas can be applied in combination with standard predicates (from two-valued logic), thus extending standard database systems for coping with missing or imprecise data.