Near-Horn Prolog (nH-Prolog) is an extension of Prolog to handle disjunction and classical negation while retaining the positive attributes of Prolog inner-loop speed is achieved; the Prolog format is also preserved by retaining a positive implication logic. Limited experience with a prototype interpreter suggest that this approach works well when there are very few "non-Prolog" (indefinite clauses. It is conjectured that many problems that fall outside the Prolog domain have very few violating clauses. The study of nH-Prolog will be continued by building a state-of-the-art compiler whose inner-loop speed closely approximates that of existing Prolog compilers. An appropriate abstract machine based on the WAM will be designed, taking advantage of nH-Prolog's similarity to Prolog. Challenging conceptual problems exist in allowing negation-as-failure to coexist with classical negation; other procedural questions arise. Standard optimization tricks can be exploited only if variant formations of nH- Prolog are possible. A parallel variant of nH-Prolog is to be designed and implemented, a project summary.