Integrity is a guarantee offered by Database Management Systems, both centralized and distributed, against nonmalicious errors in its data, i.e., the data is faithful to the relevant external world objects and their constraints. Heterogeneous distributed databases (HDDBs), by allowing shared access to pre-existing databases, are growing in importance. They exhibit site autonomy, the right of each local database to reject arbitrary global demands. Unfortunately, site autonomy seriously exacerbates global integrity maintenance. The aim of this research is to develop methods for maintaining integrity in distributed databases while accommodating site autonomy. The research plan is to explore three related techniques: generation of local sufficient constraints from global constraints, automated theorem proving, and relaxation of constraints. Some global constraints can be transformed into relatively simple, adjustable local ones needing little coordination, thus satisfying autonomy. This project investigates both the theoretical questions regarding what class of constraints is so transformable, and the p ractical question of how to produce a tool for generating such transformations. The proposed tool extends theorem proving techniques previously applied to centralized databases and allows special predicates that capture the notion of relaxation of constraint checking. This work will result in better integrity assurance in distributed databases in spite of site autonomy, with applications in decision support systems, optimization of material flow, and integration of scientific data from several sources, and other the areas where these requirements are important.