An Almost Classical Logic for Logic Programming and Nonmonotonic Reasoning
<|reference_start|>An Almost Classical Logic for Logic Programming and Nonmonotonic Reasoning: 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.<|reference_end|>
@article{bry2002an,
    title={An Almost Classical Logic for Logic Programming and Nonmonotonic
  Reasoning},
    author={Franc{c}ois Bry (University of Munich, Germany)},
    journal={arXiv preprint arXiv:cs/0207091},
    year={2002},
    archivePrefix={arXiv},
    eprint={cs/0207091},
    primaryClass={cs.LO}
}