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Mathematical logic provides a conceptual framework for many different areas of science. It has been recognized recently that logic is also significant for data bases. To focus on this impor- tant topic, a group of researchers met at a workshop in Toulouse, France on November 16-18, 1977. The workshop was held at the Centre d'Etudes et de Recherches de L'Ecole Nationale Superieure de L'Aeronautique et de L'Espace de Toulouse (C. E. R. T. ). We are pleased to acknowledge the financial support received from the Direction des Recherches, Etudes et Techniques d'Armenent (D. R. E. T) and from C. E. R. T. Without this support the workshop would not have been possible. We particularly wish to thank our friend and colleague Jean Marie Nicolas for handling much of the organi- zation of the workshop. This book is a collection of substantially revised versions of the majority of the papers presented at the workshop. Every paper was reviewed carefully by at least two reviewers. Many thanks are due to our reviewers for their detailed reading of the papers and their constructive comments. The book provides, for the first time, a comprehensive descrip- tion of the interaction between logic and data bases.