Eliminating negation from normal logic programs

Abstract

In this paper, we propose a bottom-up partial evaluation of normal programs with a top-down expansion of negated atoms to obtain equivalent logic programs. A program P is transformed to P ^ω by a bottom-up computation on the positive component of P while the negative counterpart is left untouched. During this process, we collect all substitutions describing a partial answer set to all the positive atoms in the bodies of P. The declarative semantics of P is given by the completion of P ^ω. The completed predicate definitions in P ^ω, if they do not contain local variables, can be used as a basis for expanding each negated atom in the bodies of P ^ω. We show that for a class of programs where every negative subgoal can be expanded, the resultant program P' is a definite logic program with equality and disequality constraints. If the program falls outside this class, the resultant program may be executed using Chan's SLD - CNF resolution.

Our proposed scheme provides a sound and complete query answering system for a class of programs whose positive part has a finite T ^P_ω and whose clauses satisfy the positive grounded property defined herein. With the bottom-up computation, all infinite positive loops are removed. With all the negated atoms expanded or eliminated at partial evaluation time, less work is required during the run-time query answering and problems with floundering are removed.