2002/07/25 by François Bry, Bry, François
Computer Science · #Advanced Algebra and Logic #D.3.1 #F.4.1 #FOS: Computer and information sciences #I.2.3 #I.2.4 #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #cs.LO
paper · pdf · doi:10.48550/arxiv.cs/0207091
16 pages. Originally published in proc. PCL 2002, a FLoC workshop; eds. Hendrik Decker, Dina Goldin, Jorgen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/)
arxiv created 2002/07/25 · openalex publication_date 2002/07/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The model theory of a first-order logic called N4 is introduced. N4 does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N4 is very close to classical logic: N4 has two truth values; implications in N4 are material, like in classical logic; and negation distributes over compound formulas in N4 as it does in classical logic. Results suggest that the semantics of normal logic programs is conveniently formalized in N4: Classical logic Herbrand interpretations generalize straightforwardly to N4; the classical minimal Herbrand model of a positive logic program coincides with its unique minimal N4 Herbrand model; the stable models of a normal logic program and its so-called complete minimal N4 Herbrand models coincide.