An Almost Classical Logic for Logic Programming and Nonmonotonic Reasoning.

Abstract. The model theory of a first-order logic called N 4 is introduced. N 4 does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N 4 is very close to classical logic: N 4 has two truth values; implications are, in N 4 like in classical logic, material; and negation distributes over compound formulas in N 4 as it does in classical logic. Results suggest that the semantics of normal logic programs is conveniently formalized in N 4: Classical logic Herbrand interpretations generalize straightforwardly to N 4; the classical minimal Herbrand model of a positive logic program coincides with its unique minimal N 4 Herbrand model; the stable models of a normal logic program and its so-called complete minimal N 4 Herbrand models coincide. 1