Logic Programming with Default, Weak and Strict Negations

This paper treats logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so that a soundness of the procedure is guaranteed in terms of 3-valued logic model theory.Comment: 14 pages, to appear in Theory and Practice of Logic Programming (TPLP

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

A Complete Axiomatization of the Three valued Completion of Logic Programs

We prove the completeness of extended SLDNF-resolution for the new class of e-programs with respect to the three-valued completion of a logic program. Not only the class of allowed programs but also the class of definite programs are contained in the class of ε-programs. To understand better the three-valued completion of a logic program we introduce a formal system for three-valued logic in which one can derive exactly the three-valued consequences of the completion of a logic program. The system is proof theoretically interesting, since it is a fragment of Gentzen's sequent calculus L