Knowledge discovery in databases and data mining aim at semiautomatic tools for the analysis of large data sets. It can be argued that several data mining tasks consist of locating interesting sentences from a given logic that are true in the database. Then the task of the user/analyst is to is to query this set, the theory of the database. This view gives rise to the concept of of inductive databases, i.e., databases that in addition to the data contain also inductive generalizations about the data.
We describe a rough framework for inductive databases, and consider also condensed representations, data structures that make it possible to answer queries about the inductive database approximately correctly and reasonably efficiently.