Jean-Marie Nicolas

Logic and Databases: A Deductive Approach

The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling and maintenance, query optimization, and data dependencies. The second part deals mainly with the representation and manipulation of deduced facts and incomplete information. Categories and Subject Descriptors: H.2.1 [Database Management]: Logical Design— data models; H.2.3 [Database Management]: Languages— query languages; H.2.4 [Database Management]: Systems— query processing General Terms: Deductive Databases, Indefinite Data, Logic and Databases, Null Values, Relational Databases

Logic for improving integrity checking in relational data bases

SummaryWhen an “updating” operation occurs on the current state of a data base, one has to ensure the new state obeys the integrity constraints. So, some of them have to be evaluated on this new state. The evaluation of an integrity constraint can be time consuming, but one can improve such an evaluation by taking advantage from the fact that the integrity constraint is satisfied in the current state. Indeed, it is then possible to derive a simplified form of this integrity constraint which is sufficient to evaluate in the new state in order to determine whether the initial constraint is still satisfied in this new state. The purpose of this paper is to present a simplification method yielding such simplified forms for integrity constraints. These simplified forms depend on the nature of the updating operation which is the cause of the state change. The operations of inserting, deleting, updating a tuple in a relation as well as transactions of such operations are considered. The proposed method is based on syntactical criteria and is validated through first order logic. Examples are treated and some aspects of the method application are discussed.

Data Base: Theory vs. Interpretation

This paper is concerned with the formalization of data bases in terms of first order logic concepts. Two approaches to such a formalization are first considered. In the first approach the elementary facts as well as the general statements are considered as the proper axioms of a first order theory, whereas in the second one the elementary facts are considered as defining an interpretation of a first order theory whose proper axioms are the sole general statements. These two approaches are discussed and contrasted with regard to the representation of negative information, querying and integrity checking. Both of them impose a uniform use of general statements; so, a third approach, which is an extension of the second one, is proposed. It enables one to use some general statements as derivation rules while others are used as integrity rules. Finally, due to their importance in relational data bases, some results specific to functional and multivalued dependency statements are stated.

First order logic formalization for functional, multivalued and mutual dependencies

The purpose of this paper is to show that first order logic is adequate for formalizing functional, multivalued and mutual dependencies in relational data bases. Advantages of using logic instead of tailored formal systems are presented. This paper is decomposed into four sections. The first one presents some notions of logic and theorem proving which are relevant to this study. In the second section, a way to analyze data bases in terms of logic is briefly indicated. The third section deals with the expression of dependency statements as formulas of logic. Lastly section 4 is concerned with some properties of dependency statements which follow directly from the proposed formalization.

Integrity Checking in Deductive Data Bases

This paper is concerned with the use of general laws in data bases. It consists of two main parts respectively devoted to state laws and to transition laws. Some of the state laws are used as derivation rules while others are used as integrity rules. Integrity rules as well as derivation rules can be treated in many ways which are presented. For each such method, the actions to be undertaken when querying, adding, suppressing and updating information in the data base are studied. For transition laws, a formalism is proposed which enables them to be handled in the same way as integrity rules stemming from state laws. The self-consistency of transition laws is also discussed.

Logic and databases: an assessment

The field of “Logic or Deductive Databases” has now reached maturity. We have been fortunate, in the past, to report on the status of this field in its infancy [18] and, later, in its adolescence [17, 19]. An account of its history has recently been given by Jack Minker in [26]. This field is now well established and forms a large body of research across the world as attested by the sessions devoted to it in most Database, as well as Logic Programming conferences. In this short paper we would like to briefly sketch its current status both from a theoretical and a practical viewpoint. This paper is definitely neither an overview nor a survey (for such a survey see the quite recent book by Ceri, Gottlob and Tanca [11]), but it merely expresses our view of the current status of the field strongly biased by the work conducted at ECRC over the last six years or so. This biased presentation means in no ways that we want to ignore or minimize the importance of the contribution to the evolution of this field of many other laboratories in the world, among which we would like to explicitly mention MCC, ICOT and the many ESPRIT related projects all over Europe.

Can We Reach a Uniform Paradigm for Deductive Query Evaluation

During the 1980s we have seen the rise of an exciting new discipline of computed science, called logic programming. The most prominent representative of this new programming paradigm is the language PROLOG, developed in the early 1970s by Colmerauer in Marseille and Kowalski in Edinburgh. Programming in PROLOG differs from conventional programming both stylistically as well as computationally, as it uses logic to represent knowledge and deduction to solve problems. Due to the success of PROLOG in the academic world, logic programming today slowly begins to find its way out of the research labs into advanced products and systems like expert system shells or knowledge-based systems.

How to look at deductive databases

After positioning deductive databases within the spectrum of knowledge-based systems, this paper briefly discusses their functionalities and some possible architectures while stressing the fact that the appropriate engineering skill to build them is not yet fully available.

Background for Advances in Data Base Theory

The intent of this chapter is to provide appropriate background for the reader so that he can comprehend more readily the advances in data base theory described in the chapters to follow. Following this introductory chapter there are three major subdivisions in the book: Data Base Design; General Laws: Deduction and Integrity; and Informative Capabilities for Users. For each area we provide background material on the subject matter, related work that has taken place in the particular subject, and’ provide an overview of the essential aspects of each paper that appears in the section.