In this article, we address the problem of changing the constraints of a mediated schema to accommodate the set of constraints of a new export schema. The relevance of this problem lies in that the constraints of a mediated schema capture the common semantics of the data sources and, as such, they must be maintained and made available to the users of the mediation environment. We first argue that such problem can be solved by computing the greatest lower bound of two theories induced by sets of constraints, defined as the intersection of the theories. Then, for an expressive family of conceptual schemas, we show how to efficiently decide logical implication and how to compute the greatest lower bound of two theories induced by sets of constraints. The family of conceptual schemas we work with partly corresponds to OWL Lite and supports the equivalent of named classes, datatype and object properties, minCardinalities and maxCardinalities, InverseFunctionalProperties, subset constraints, and disjointness constraints. Such schemas are also sufficiently expressive to encode commonly used UML constructs, such as classes, attributes, binary associations without association classes, cardinality of binary associations, multiplicity of attributes, and ISA hierarchies with disjointness, but not with complete generalizations.
