Logic and Data Bases PDF
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LOGIC AND DATABASES LOGIC AND DATABASES Edited by Herve Gallaire Centre d'Etudes et de Recherches de Toulouse Toulouse, France and .Jack Minker University of Maryland College Park, Maryland PLENUM PRESS · NEW YORK AND LONDON Library of Congress Cataloging in Publication Data Symposium on Logic and Data Bases, Centre d'etudes etde recherches de Toulouse, 1977. Logic and data bases. Includes indexes. 1. Data base management - Congresses. 2. Logic, Symbolic and mathematical - Con gresses. I. Gallaire, Herve. II. Minker, Jack. III. Title. QA 76.9.D3S97 001.6'42 78-14032 ISBN-13: 978-1-4684-3386-9 e-ISBN-13: 978-1-4684-3384-5 DOl: 10.1007/978-1-4684-3384-5 First Printing-November 1978 Second Printing-June 1984 The content of this volume is based on the proceedings of the Symposium on Logic and Data Bases 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.), Toulouse, France, November 16-18, 1977 © 1978 Plenum Press, New York A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 Softcover reprint of the hardcover 1s t edition 1978 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher FOREWORD 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. It 'will be seen that logic can be used as a programming language, as a query language, to perform deductive searches, to maintain the integrity of data bases, to provide a formalism for handling negative infor mation, to generalize concepts in knowledge representation, and to represent and manipulate data structures. Thus, logic provides a powerful tool for data bases that is accomplished by no other approach developed to date. It provides a unifying mathematical theory for data bases. In our introductory article we describe the important concepts of logic and relational data bases that are needed for the remaining chapters, and provide an overview of the major ideas set forth by the authors. We believe that the book can be used as the basis for a graduate course in computer science. For this purpose, the student should have a firm background in mathematical logic. It would be v vi FOREWORD desirable, but not essential, that the student have a first course in data base systems and in heuristic methods. Although we have included some background in our introductory article, the instructor will want to expand slightly on the funda mentals of resolution theorem proving and the relational data base model. This can be accomplished in the first few weeks of the semester. The chapters in the book are presented in a preferred sequence. In addition to the introductory chapter there are five major sec tions in the book. The first section discusses how data bases may be viewed in the framework of mathematical logic. The second section discusses the use of mathematical logic to represent know ledge and to perform deduction. How one can deal with negative information is described in the third section and in the section, "Data Bases Viewed Through Logic", in articles by Reiter and by Nicolas and Gallaire. Logic and data base integrity is the sub ject of the fourth section. Finally, some applications and a description of how existing query languages relate to logic is described in the last section. The instructor can select indi~ vidual chapters from the book for reading depending upon the topics he wishes to stress. We wish to express our grateful appreciation to Mrs. Pat Young for her work and devotion to the book. She handled all correspon dence with the authors and referees, typed the entire book and helped to organize the index. H. GALLAIRE J. MINKER August 1978 CONTENTS FOREWORD INTRODUCTION An Ov~view and Introduction to Logic and Data Bases, 3 H. Gallaire, J. Minker, and J. M. Nicolas DATA BASES VIEWED THROUGH FORMAL LOGIC Data Base: Theory vs. Interpretation, J. M. Nicolas 33 and H. Gallaire On Closed WorZd Data Bases, R. Reiter 55 Logic for Data Description, R. Kowalski 77 KNOWLEDGE AND DEDUCTION REPRE8EN~TION An Experimental Relational Data Base System Based on 107 Logic, J. Minker Deductive Question-Answering on ReZational Data Bases, 149 R. Reiter Deductive Planning and Pathfinding for ReZational Data 179 Bases, C. Kellogg, P. Klahr, and L. Travis DEDUCE 2: Further Investigations of Deduction in 201 Relational Data Bases, C. L. Chang Nondeterministic Languages Used for the Definition 237 of Data Models, M. Colombetti, P. Paolini, and G. Pelagatti An Axiorratic Data Base Theory, 8-A. Tl1rnlund 259 vii viii CONTENTS NEGATIVE INFORMATION AND DATA BASES Negation as FaiZure, K. L. Clark 293 LOGIC AND DATA BASE INTEGRITY Integrity Checking in Deductive Data Bases 325 3 J. M. Nicolas and K. Yazdanian QUERY LANGUAGES AND APPLICATIONS The AppZication of PROLOG to the DeveZopment of Q4 347 and DBM Systems I. Fut6, F. Darvas, and P. Szeredi 3 The Predicate CaZcuZus-Language KS as a Query Language 377 3 W. Dilger and G. Zifonun High LeveZ Data Base Query Languages A. Pirotte 409 3 AUTHOR INDEX 437 SUBJECT INDEX 441 List of Referees 455 Addresses of Contributing Authors 457 INTRODUCTION AN OVERVIEW AND INTRODUCTION TO LOGIC AND DATA BASES Herve Gallairel , Jack Minker2 and Jean Marie Nicolasl ONERA-CERT, Toulouse, Francel University of Maryland, College Park, Maryland2 ABSTRACT In this introductory chapter we provide both an overview of mathematical logic and relational data base concepts that serve as background for the book, as well as an introduction to the major ideas discussed in the individual chapters. The first section of this paper is devoted to a description of first order logic, while the second describes the relational data base model. The next sections summarize the five major units of chapters. The theme of this collection is that mathematical logic pro vides a conceptual framework for data base systems. The first unit demonstrates this, showing explicitly how data base concepts can be analyzed in terms of formal logic, and provides a charac terization of the hypothetical worlds on which data base systems work. The second analyzes knowledge representation and how it relates to the process of deduction; alternate approaches are described and their advantages and limitations are noted. The third considers how logic may be used to express constraints on a data base and to maintain data base integrity. A similar approach proves useful in dealing with the fourth topic - meaning assigned to answers when negative questions are posed. The last demon strates how logic provides a unifying framework for query lan guage. 3 4 GALLA IRE , MINKER AND NICOLAS INTRODUCTION Mathematical logic has been applied to many different areas, including that of data bases. The material presented in this book shows how logic can be used to express and to solve many fundamen tally difficult problems, and for understanding data bases. The chapters are grouped into broad classes corresponding to the five main topics treated in this book. The first set of papers focuses on the analysis of data base concepts in terms of formal logic, and provides a characterization of the hypothetical worlds on which data base systems work. The second considers knowledge representation as it relates to the pro cess of deducing facts implicit in the data base; alternate ap proaches and their limitations are presented. The third describes how logic may be viewed so as to express and to maintain data base integrity. A similar view proves useful in dealing with the fourth topic, namely describing how meaning can be assigned to answers to negative questions. The final topic studies existing and proposed query languages for relational data base systems, demonstrating how logic provides a unifying framework for such languages. LOGICAL SYSTEMS The material in this section p~ovides a brief overview of logic as it relates to this book. The reader who would like a more detailed description should refer to the books by Chang and Lee [1973] and by Mendelson [1964]. A logical system can be defined from two different, but equi valent viewpoints: the semantic view, and the syntactic view. Both approaches are founded upon first defining a language - a col lection of symbols and of rules for building well-formed formulas (wffs) • The Language of First Order Logic - Syntax The language used throughout the book is that of the first order predicate calculus. The language consists of the following primitive symbols: variable and constant symbols which will be denoted by lowercase letters taken from the end of the alphabet for variable symbols, and from the beginning of the alphabet for constant symbols; function symbols denoted by lower case symbols f, g, and h;
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