How well are non-horn clauses handled?

Abstract

We analyze the search space of two clause-based proof procedures, the Model Elimination procedure and Near-Horn Prolog, both of Loveland. We study how the search space changes with respect to the degree of how “non-Horn” a clause set is. The “non-Hornness” of a clause set is measured by the average number of negative subgoals in a clause. We show that Near-Horn Prolog performs better at the very beginning of the “non-Hornness” scale. But when the clause set becomes more and more non-Horn, model elimination has a clear advantage over Near-Horn Prolog. We also observe an interesting symmetrical property of the search space of model elimination. The reason for this symmetry is that model elimination treats positive literals and negative literals in the same way.