The author proposes an extension to Prolog that handles clause sets that are Horn and almost-Horn in a manner that emphasizes clarity, efficiency, and minimal deviation from standard prolog. Although one version of near-Horn Prolog is complete under appropriate search strategies, we focus on incomplete variants that allow fast processing. Negation in the program is handled correctly, although within a positive implication logic extension of Horn logic. Processing speed degradation is directly proportional to the distance the program is from a Horn clause set. (AUTHOR)