Extending and implementing the stable model semantics
Artificial Intelligence
Developing a Declarative Rule Language for Applications in Product Configuration
PADL '99 Proceedings of the First International Workshop on Practical Aspects of Declarative Languages
Stable Model Semantics of Weight Constraint Rules
LPNMR '99 Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning
Two-Literal Logic Programs and Satisfiability Representation of Stable Models: A Comparison
AI '02 Proceedings of the 15th Conference of the Canadian Society for Computational Studies of Intelligence on Advances in 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
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
A Constructive semantic characterization of aggregates in answer set programming
Theory and Practice of Logic Programming
Well-founded and stable semantics of logic programs with aggregates
Theory and Practice of Logic Programming
Logic programs with monotone abstract constraint atoms*
Theory and Practice of Logic Programming
Lparse Programs Revisited: Semantics and Representation of Aggregates
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Stable models and difference logic
Annals of Mathematics and Artificial Intelligence
SAT-based answer set programming
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Logic programs with abstract constraint atoms
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Computing Stable Models via Reductions to Difference Logic
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Weight Constraint Programs with Functions
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Level Mapping Induced Loop Formulas for Weight Constraint and Aggregate Programs
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
The Conflict-Driven Answer Set Solver clasp: Progress Report
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
A generalized gelfond-lifschitz transformation for logic programs with abstract constraints
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
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
Answer sets for logic programs with arbitrary abstract constraint atoms
Journal of Artificial Intelligence Research
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
The first answer set programming system competition
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Answer sets for propositional theories
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
SMODELSA: a system for computing answer sets of logic programs with aggregates
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
Weight constraint programs with evaluable functions
Annals of Mathematics and Artificial Intelligence
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Level mapping and loop formulas are two different means to justify and characterize answer sets for normal logic programs. Both of them specify conditions under which a supported model is an answer set. Though serving a similar purpose, in the past the two have been studied largely in isolation with each other. In this paper, we study level mapping and loop formulas for weight constraint and aggregate (logic) programs. We show that, for these classes of programs, loop formulas can be devised from level mapping characterizations. First, we formulate a level mapping characterization of stable models and show that it leads to a new formulation of loop formulas for arbitrary weight constraint programs, without using any new atoms. This extends a previous result on loop formulas for weight constraint programs, where weight constraints contain only positive literals. Second, since aggregate programs are closely related to weight constraint programs, we further use level mapping to characterize the underlying answer set semantics based on which we formulate loop formulas for aggregate programs. The main result is that for aggregate programs not involving the inequality comparison operator, the dependency graphs can be built in polynomial time. This compares to the previously known exponential time method.