One of the most challenging problems in data manipulation in the future is to be able to efficiently handle very large databases but also multiple induced properties or generalizations in that data. Popular examples of useful properties are association rules, and inclusion and functional dependencies. Our view of a possible approach for this task is to specify and query inductive databases, which are databases that in addition to data also contain intensionally defined generalizations about the data. We formalize this concept and show how it can be used throughout the whole process of data mining due to the closure property of the framework. We show that simple query languages can be defined using normal database terminology. We demonstrate the use of this framework to model typical data mining processes. It is then possible to perform various tasks on these descriptions like, e.g., optimizing the selection of interesting properties or comparing two processes.