Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
On the declarative semantics of deductive databases and logic programs
Foundations of deductive databases and logic programming
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Default theories that always have extensions
Artificial Intelligence
Extending and implementing the stable model semantics
Artificial Intelligence
Comparing the Expressive Powers of Some Syntactically Restricted Classes of Logic Programs
CL '00 Proceedings of the First International Conference on Computational Logic
Nonmonotonic reasoning: towards efficient calculi and implementations
Handbook of automated reasoning
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
Why are there so many loop formulas?
ACM Transactions on Computational Logic (TOCL)
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
Answer Set Programming Based on Propositional Satisfiability
Journal of Automated Reasoning
Elementary sets for logic programs
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
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
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
Conflict, consistency and truth-dependencies in graph representations of answer set logic programs
GKR'11 Proceedings of the Second international conference on Graph Structures for Knowledge Representation and Reasoning
Inductive definitions in constraint programming
ACSC '13 Proceedings of the Thirty-Sixth Australasian Computer Science Conference - Volume 135
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Loops and the corresponding loop formulas play an important role in answer set programming. On the one hand, they are used for guaranteeing correctness and completeness in SAT-based answer set solvers. On the other hand, they can be used by conventional answer set solvers for finding unfounded sets of atoms. Unfortunately, the number of loops is exponential in the worst case. We demonstrate that not all loops are actually needed for answer set computation. Rather, we characterize the subclass of elementary loops and show that they are sufficient and necessary for selecting answer sets among the models of a program's completion. Given that elementary loops cannot be distinguished from general ones in atom dependency graphs, we show how the richer graph structure provided by body-head dependency graphs can be exploited for this purpose.