  The formalism of active integrity constraints was introduced as a way to
specify particular classes of integrity constraints over relational databases
together with preferences on how to repair existing inconsistencies. The
rule-based syntax of such integrity constraints also provides algorithms for
finding such repairs that achieve the best asymptotic complexity. However, the
different semantics that have been proposed for these integrity constraints all
exhibit some counter-intuitive examples. In this work, we look at active
integrity constraints using ideas from algebraic fixpoint theory. We show how
database repairs can be modeled as fixpoints of particular operators on
databases, and study how the notion of grounded fixpoint induces a
corresponding notion of grounded database repair that captures several natural
intuitions, and in particular avoids the problems of previous alternative
semantics. In order to study grounded repairs in their full generality, we need
to generalize the notion of grounded fixpoint to non-deterministic operators.
We propose such a definition and illustrate its plausibility in the database
context.
