  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 in N^4 are material, like in classical logic; 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.
