Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
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
Nested expressions in logic programs
Annals of Mathematics and Artificial Intelligence
Enhancing disjunctive logic programming systems by SAT checkers
Artificial Intelligence
Theory and Practice of Logic Programming
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
Unfolding partiality and disjunctions in stable model semantics
ACM Transactions on Computational Logic (TOCL)
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)
SAT-based answer set programming
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Elementary sets for logic programs
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
On Reductive Semantics of Aggregates in Answer Set Programming
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Loop formulas for logic programs with arbitrary constraint atoms
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Properties and applications of programs with monotone and convex constraints
Journal of Artificial Intelligence Research
A new perspective on stable models
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
On the equivalence between answer sets and models of completion for nested logic programs
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Modularity aspects of disjunctive stable models
Journal of Artificial Intelligence Research
A model-theoretic counterpart of loop formulas
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Loop formulas for circumscription
Artificial Intelligence
Head-elementary-set-free logic programs
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
FoIKS'08 Proceedings of the 5th international conference on Foundations of information and knowledge systems
Stable models and circumscription
Artificial Intelligence
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
CMODELS: SAT-based disjunctive answer set solver
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
First-order stable model semantics and first-order loop formulas
Journal of Artificial Intelligence Research
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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 HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.