TY - JOUR
A1 - Gebser, Martin
A1 - Lee, Joohyung
A1 - Lierler, Yuliya
T1 - On elementary loops of logic programs
T2 - Theory and practice of logic programming
N2 - Using the notion of an elementary loop, Gebser and Schaub (2005. Proceedings of the Eighth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05), 53-65) refined the theorem on loop formulas attributable to Lin and Zhao (2004) by considering loop formulas of elementary loops only. In this paper, we reformulate the definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we also show that the corresponding problem is coNP-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs attributable to Ben-Eliyahu and Dechter (1994. Annals of Mathematics and Artificial Intelligence 12, 53-87). Like an Ha: program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.
KW - stable model semantics
KW - loop formulas
KW - unfounded sets
Y1 - 2011
UR - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/36524
SN - 1471-0684 (print)
VL - 11
IS - 2
SP - 953
EP - 988
PB - Cambridge Univ. Press
CY - New York
ER -