The Complexity of Local Stratification

The class of locally stratified logic programs is shown to be Π11-complete by the construction of a reducibility of the class of infinitely branching nondeterministic finite register machines.nondeterministic finite register machines

Logic Programming as Constructivism

The features of logic programming that seem unconventional from the viewpoint of classical logic can be explained in terms of constructivistic logic. We motivate and propose a constructivistic proof theory of non-Horn logic programming. Then, we apply this formalization for establishing results of practical interest. First, we show that 'stratification can be motivated in a simple and intuitive way. Relying on similar motivations, we introduce the larger classes of 'loosely stratified' and 'constructively consistent' programs. Second, we give a formal basis for introducing quantifiers into queries and logic programs by defining 'constructively domain independent* formulas. Third, we extend the Generalized Magic Sets procedure to loosely stratified and constructively consistent programs, by relying on a 'conditional fixpoini procedure

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

Updates by Reasoning about States

It has been argued that some sort of control must be introduced in order to perform update operations in deductive databases. Indeed, many approaches rely on a procedural semantics of rule based languages and often perform updates as side-effects. Depending on the evaluation procedure, updates are generally performed in the body (top-down evaluation) or in the head of rules (bottom-up evaluation). We demonstrate that updates can be specified in a purely declarative manner using standard model based semantics without relying on procedural aspects of program evaluation. The key idea is to incorporate states as first-class objects into the language. This is the source of the additional expressiveness needed to define updates. We introduce the update language Statelog+-, discuss various domains of application and outline how to implement computation of the perfect model semantics for Statelog+- programs

A comparison between algebraic query languages for flat and nested databases

AbstractRecently, much attention has been paid to query languages for nested relations. In the present paper, we consider the nested algebra and the powerset algebra, and compare them both mutually as well as to the traditional flat algebra. We show that either nest or difference can be removed as a primitive operator in the powerset algebra. While the redundancy of the nest operator might have been expected, the same cannot be said of the difference. Basically, this result shows that the presence of one nonmonotonic operator suffices in the powerset algebra. As an interesting consequence of this result, the nested algebra without the difference remains complete in the sense of Bancilhon and Paredaens. Finally, we show there are both similarities and fundamental differences between the expressiveness of query languages for nested relations and that of their counterparts for flat relations