Query Evaluation in Deductive Databases

It is desirable to answer queries posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing. However, the classical fixpoint procedures based on bottom-up processing — the naive and semi-naive methods — are rather primitive and often inefficient. In this article, we rely on bottom-up meta-interpretation for formalizing a new fixpoint procedure that performs a different kind of reasoning: We specify a top-down query answering method, which we call the Backward Fixpoint Procedure. Then, we reconsider query evaluation methods for recursive databases. First, we show that the methods based on rewriting on the one hand, and the methods based on resolution on the other hand, implement the Backward Fixpoint Procedure. Second, we interpret the rewritings of the Alexander and Magic Set methods as specializations of the Backward Fixpoint Procedure. Finally, we argue that such a rewriting is also needed in a database context for implementing efficiently the resolution-based methods. Thus, the methods based on rewriting and the methods based on resolution implement the same top-down evaluation of the original database rules by means of auxiliary rules processed bottom-up

Proving Finite Satisfiability of Deductive Databases

It is shown how certain refutation methods can be extended into semi-decision procedures that are complete for both unsatisfiability and finite satisfiability. The proposed extension is justified by a new characterization of finite satisfiability. This research was motivated by a database design problem: Deduction rules and integrity constraints in definite databases have to be finitely satisfiabl

Computing only minimal answers in disjunctive deductive databases

A method is presented for computing minimal answers in disjunctive deductive databases under the disjunctive stable model semantics. Such answers are constructed by repeatedly extending partial answers. Our method is complete (in that every minimal answer can be computed) and does not admit redundancy (in the sense that every partial answer generated can be extended to a minimal answer), whence no non-minimal answer is generated. For stratified databases, the method does not (necessarily) require the computation of models of the database in their entirety. Compilation is proposed as a tool by which problems relating to computational efficiency and the non-existence of disjunctive stable models can be overcome. The extension of our method to other semantics is also considered.Comment: 48 page

Perspectives in deductive databases

AbstractI discuss my experiences, some of the work that I have done, and related work that influenced me, concerning deductive databases, over the last 30 years. I divide this time period into three roughly equal parts: 1957–1968, 1969–1978, 1979–present. For the first I describe how my interest started in deductive databases in 1957, at a time when the field of databases did not even exist. I describe work in the beginning years, leading to the start of deductive databases about 1968 with the work of Cordell Green and Bertram Raphael. The second period saw a great deal of work in theorem providing as well as the introduction of logic programming. The existence and importance of deductive databases as a formal and viable discipline received its impetus at a workshop held in Toulouse, France, in 1977, which culminated in the book Logic and Data Bases. The relationship of deductive databases and logic programming was recognized at that time. During the third period we have seen formal theories of databases come about as an outgrowth of that work, and the recognition that artificial intelligence and deductive databases are closely related, at least through the so-called expert database systems. I expect that the relationships between techniques from formal logic, databases, logic programming, and artificial intelligence will continue to be explored and the field of deductive databases will become a more prominent area of computer science in coming years

Integrity constraints in deductive databases

A deductive database is a logic program that generalises the concept of a relational database. Integrity constraints are properties that the data of a database are required to satisfy and in the context of logic programming, they are expressed as closed formulae. It is desirable to check the integrity of a database at the end of each transaction which changes the database. The simplest approach to checking integrity in a database involves the evaluation of each constraint whenever the database is updated. However, such an approach is too inefficient, especially for large databases, and does not make use of the fact that the database satisfies the constraints prior to the update. A method, called the path finding method, is proposed for checking integrity in definite deductive databases by considering constraints as closed first order formulae. A comparative evaluation is made among previously described methods and the proposed one. Closed general formulae is used to express aggregate constraints and Lloyd et al. 's simplification method is generalised to cope with these constraints. A new definition of constraint satisfiability is introduced in the case of indefinite deductive databases and the path finding method is generalised to check integrity in the presence of static constraints only. To evaluate a constraint in an indefinite deductive database to take full advantage of the query evaluation mechanism underlying the database, a query evaluator is proposed which is based on a definition of semantics, called negation as possible failure, for inferring negative information from an indefinite deductive database. Transitional constraints are expressed using action relations and it is shown that transitional constraints can be handled in definite deductive databases in the same way as static constraints if the underlying database is suitably extended. The concept of irnplicit update is introduced and the path finding method is extended to compute facts which are present in action relations. The extended method is capable of checking integrity in definite deductive databases in the presence of transitional constraints. Combining different generalisations of the path finding method to check integrity in deductive databases in the presence of arbitrary constraints is discussed. An extension of the data manipulation language of SQL is proposed to express a wider range of integrity constraints. This class of constraints can be maintained in a database with the tools provided in this thesis

Towards Intelligent Databases

This article is a presentation of the objectives and techniques of deductive databases. The deductive approach to databases aims at extending with intensional definitions other database paradigms that describe applications extensionaUy. We first show how constructive specifications can be expressed with deduction rules, and how normative conditions can be defined using integrity constraints. We outline the principles of bottom-up and top-down query answering procedures and present the techniques used for integrity checking. We then argue that it is often desirable to manage with a database system not only database applications, but also specifications of system components. We present such meta-level specifications and discuss their advantages over conventional approaches