Over the past several decades, the study of conjunctive queries has occupied a central place in the theory and practice of database systems. In recent years, conjunctive queries have played a prominent role in the design and use of schema mappings for data integration and data exchange tasks. In this paper, we investigate several different aspects of conjunctive-query equivalence in the context of schema mappings and data exchange. In the first part of the paper, we introduce and study a notion of a local transformation between database instances that is based on conjunctive-query equivalence. We show that the chase procedure for GLAV mappings (that is, schema mappings specified by sourceto-target tuple-generating dependencies) is a local transformation with respect to conjunctive-query equivalence. This means that the chase procedure preserves bounded conjunctive-query equivalence, that is, if two source instances are indistinguishable using conjunctive queries of a sufficiently l...
Ronald Fagin, Phokion G. Kolaitis