Conceptual integrity is required for the result of data integration to be cohesive and sensible. Compromised conceptual integrity results in "semantic faults," which are commonly blamed for latent integration bugs. A logical model of conceptual integrity in data integration and a simple example application are presented. Unlike constructive models that attempt to prevent semantic faults, this model allows both correct and incorrect integrations to be described. Imperfect legacy systems can therefore be modeled, allowing a more formal analysis of their flaws and the possible remedies.