Resolution for Logic Programming with Universal Quantifiers

It is clearly desirable that logical specifications and the programs that implement them should be as close as possible. Such a claim is often made in support of the logic programming paradigm. However, SLD-resolution, the basic procedural semantics for logic programming, is only defined for programs whose statements are Horn clauses. Most research for extending the Horn clause framework has been concerned with allowing negative literals in the bodies of the statements where SLD-resolution is extended with negation-as-failure. However, one of the main components of first order logic not allowed in clauses is (explicit) quantification. This paper addresses this problem by showing how SLD-resolution can be extended to allow for universally quantified implication formulas as conjuncts in the body of the statements. It will be shown that this technique includes negation-as-failure as a degenerate case.