Towards Query Evaluation in Inductive Databases Using Version Spaces

An inductive query specifies a set of constraints that patterns should satisfy. We study a novel type of inductive query that consists of arbitrary boolean expressions over monotonic and anti-monotonic primitives. One such query asks for all patterns that have a frequency of at least 50 on the positive examples and of at most 3 on the negative examples. We investigate the properties of the solution spaces of boolean inductive queries. More specifically, we show that the solution space w.r.t. a conjunctive query is a version space, which can be represented by its border sets, and that the solution space w.r.t. an arbitrary boolean inductive query corresponds to a union of version spaces. We then discuss the role of operations on version spaces (and their border sets) in computing the solution space w.r.t. a given query. We conclude by formulating some thoughts on query optimization.