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

Incorporating Stratified Negation into Query-Subquery Nets for Evaluating Queries to Stratified Deductive Databases

Most of the previously known evaluation methods for deductive databases are either breadth-first or depth-first (and recursive). There are cases when these strategies are not the best ones. It is desirable to have an evaluation framework for stratified DatalogN that is goal-driven, set-at-a-time (as opposed to tuple-at-a-time) and adjustable w.r.t. flow-of-control strategies. These properties are important for efficient query evaluation on large and complex deductive databases. In this paper, by incorporating stratified negation into so-called query-subquery nets, we develop an evaluation framework, called QSQNSTR, with such properties for evaluating queries to stratified DatalogN databases. A variety of flow-of-control strategies can be used for QSQNSTR. The generic evaluation method QSQNSTR for stratified DatalogN is sound, complete and has a PTIME data complexity