An Almost Classical Logic for Logic Programming and Nonmonotonic Reasoning

Details An Almost Classical Logic for Logic Programming and Nonmonotonic Reasoning An Almost Classical Logic for Logic Programming and Nonmonotonic Reasoning

2002-07-25

arxiv.org/abs/cs/0207091v1

Computer Science

Logic in Computer Science

16 pages. Originally published in proc. PCL 2002, a FLoC workshop; eds. Hendrik Decker, Dina Goldin, Jorgen Villadsen, Toshiha

Scientific paper

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.

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