Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
Signed data dependencies in logic programs
Journal of Logic Programming
Negation by default and unstratifiable logic programs
Selected papers of the workshop on Deductive database theory
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Tie-breaking semantics and structural totality
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On the relations between stable and well-founded semantics of logic programs
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
Proceedings of the eleventh international conference on Logic programming
A three-valued semantics for deductive databases and logic programs
Journal of Computer and System Sciences
Reasoning with minimal models: efficient algorithms and applications
Artificial Intelligence
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
Abduction in logic programming: a new definition and an abductive procedure based on rewriting
Artificial Intelligence
ASSAT: computing answer sets of a logic program by SAT solvers
Eighteenth national conference on Artificial intelligence
Consistency property of finite FC-normal logic programs
Journal of Computer Science and Technology
Answer-set programming with bounded treewidth
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Using ASP for knowledge management with user authorization
Data & Knowledge Engineering
Backdoors to tractable answer-set programming
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
The good, the bad, and the odd: cycles in answer-set programs
ESSLLI'10 Proceedings of the 2010 international conference on New Directions in Logic, Language and Computation
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
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An odd cycle of a logic program is a simple cycle that has an odd number of negative edges in the dependency graph of the program. Similarly, an even cycle is one that has an even number of negative edges. For a normal logic program that has no odd cycles, while it is known that such a program always has a stable model, and such a stable model can be computed in polynomial time, we show in this paper that checking whether an atom is in a stable model is NP-complete, and checking whether an atom is in all stable models is co-NP complete, both are the same as in the general case for normal logic programs. Furthermore, we show that if a normal logic program has exactly one odd cycle, then checking whether it has a stable model is NP-complete, again the same as in the general case. For normal logic programs with a fixed number of even cycles, we show that there is a polynomial time algorithm for computing all stable models. Furthermore, this polynomial time algorithm can be improved significantly if the number of odd cycles is also fixed.