Constructive Negation in CLP(H)

Inclusion of negation into logic programs is considered traditionally to be painful as the incorporation of full logic negation tends to super-exponential time complexity of the prover. Therefore the alternative approaches to negation in logic programs are studied and among them, the procedural negation as failure sounds to be the most successful and the most widely used. However, with the spread of Constraint Logic Programming (CLP), a different approach called constructive negation becomes more popular. The reasons for acceptance of constructive negation are the preservation of the advantages of the negation as failure, i.e., efficiency and handling special features of the language, and, at the same time, while removing the main drawbacks, i.e., handling ground negative subgoals and usage as a test only. In this paper we present a constructive approach to negation in logic programs. We concentrate on implementation aspects of constructive negation here, i.e., on the design of CLP(H) system, where H is the Herbrand Universe. According to the CLP approach, we use equalities and disequalities to process unification and negation. We describe a constraint solver for solving equality and disequality constraints over the Herbrand Universe and we propose a unique filtering system to obtain relevant solutions. Finally, we combine the constraint solver with the filtering system to implement the constructive negation efficiently. The presented approach to constructive negation is justified by an implementation work.