The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Disjunctive stable models: unfounded sets, fixpoint semantics, and computation
Information and Computation
Stable models and non-determinism in logic programs with negation
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
SAT-based answer set programming
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
A model-theoretic counterpart of loop formulas
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
A meta-programming technique for debugging answer-set programs
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Characterising equilibrium logic and nested logic programs: Reductions and complexity1,2
Theory and Practice of Logic Programming
Head-elementary-set-free logic programs
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Advanced techniques for answer set programming
ICLP'07 Proceedings of the 23rd international conference on Logic programming
FoIKS'08 Proceedings of the 5th international conference on Foundations of information and knowledge systems
Symmetry-breaking answer set solving
AI Communications - Answer Set Programming
On elementary loops of logic programs
Theory and Practice of Logic Programming
First-order stable model semantics and first-order loop formulas
Journal of Artificial Intelligence Research
Conflict-driven answer set solving: From theory to practice
Artificial Intelligence
On the tractability of minimal model computation for some CNF theories
Artificial Intelligence
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By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark's completion that satisfy the loop formulas of all loops. Recently, Gebser and Schaub showed that the Lin-Zhao theorem remains correct even if we restrict loop formulas to a special class of loops called "elementary loops." In this paper, we simplify and generalize the notion of an elementary loop, and clarify its role. We propose the notion of an elementary set, which is almost equivalent to the notion of an elementary loop for nondisjunctive programs, but is simpler, and, unlike elementary loops, can be extended to disjunctive programs without producing unintuitive results. We show that the maximal unfounded elementary sets for the "relevant" part of a program are exactly the minimal sets among the nonempty unfounded sets. We also present a graph-theoretic characterization of elementary sets for nondisjunctive programs, which is simpler than the one proposed in (Gebser & Schaub 2005). Unlike the case of nondisjunctive programs, we show that the problem of deciding an elementary set is coNP-complete for disjunctive programs.