Inductive databases (IDBs) contain both data and patterns. Knowledge discovery processes can be viewed as sequences of inductive queries to such databases, where inductive queries can perform both data selection and data mining. Inductive queries consist of conjunctions of primitive constraints that have to be satisfied by target patterns. The constraints can be different for different pattern domains.

Many pattern domains, mostly concerning the discovery of frequent patterns, have been considered separately: these include the domains of frequent itemsets, episodes, Datalog queries, sequences, and molecular fragments. Here we consider inductive queries in the pattern domain of polynomial equations and present a heuristic solver for this domain. We first evaluate the use of this solver on standard regression problems, then proceed to illustrate the use of constraints in discovering dynamics. We finally consider IDBs containing both the pattern domains of equations and molecular fragments, as well as combining them in order to derive QSAR (Quantitative Structure-Activity Relationships) models.