Constructive negation by bottom-up computation of literal answers

• Authors: Javier Álvez;Paqui Lucio;Fernando Orejas
• Venue: Proceedings of the 2004 ACM symposium on Applied computing
• Year: 2004

In this paper, we present a new proposal for an efficient implementation of constructive negation. In our approach the answers for a literal are bottom-up computed by solving equality constraints, instead of by handling frontiers of subsidiary computation trees. The required equality constraints are given by Shepherdson's operators which are, in a sense, similar to bottom-up immediate consequence operators. However, in order to make the procedure efficient two main techniques are applied. First, we restrict our constraints to a class of success-answers (resp. fail-answers) which are easy to manipulate and to solve (or to prove their unsatisfiability). And, second, we take advantage of the monotonic nature of Shepherdson's operators to make the procedure incremental and to avoid recalculations that are typical in frontiers-based methods. Then, goal computation is made in the usual top-down CLP scheme of collecting the answers for the selected literal into the constraint of the goal. The procedural mechanism for constructive negation is designed not only to generate every correct answer of a goal, but also to detect failure. That is, in spite of the bottom-up nature of the calculation of literal answers, goal computation is not necessarily infinite. The operational semantics that makes use of these ideas, called BCN, is sound and complete with respect to three-valued program completion for the whole class of normal logic programs. A prototype implementation of this approach has been developed and the experimental results are very promising.