Fixpoint semantics for active integrity constraints

In this paper, we apply approximation fixpoint theory, an abstract, algebraic framework designed to unify semantics of non-monotonic logics, to the field of AICs. This results in a new family of semantics for AICs. We study properties of our new semantics and relationships to existing semantics. In particular, we argue that two of the newly defined semantics stand out. Grounded repairs have a simple definition that is purely based on semantic principles that semantics for AICs should adhere to. And, as we show, they coincide with the intended interpretation of AICs on many examples. The second semantics of interest is the AFT-well-founded semantics: it is a computationally cheap semantics that provides upper and lower bounds for many other classes of repairs.