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
Complexity and expressive power of logic programming
ACM Computing Surveys (CSUR)
Extending and implementing the stable model semantics
Artificial Intelligence
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates
Proceedings of the 17th International Conference on Logic Programming
Representing Knowledge in A-Prolog
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
Enhancing disjunctive logic programming systems by SAT checkers
Artificial Intelligence
Comparisons and computation of well-founded semantics for disjunctive logic programs
ACM Transactions on Computational Logic (TOCL)
Declarative and computational properties of logic programs with aggregates
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
A model-theoretic counterpart of loop formulas
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Answer sets for propositional theories
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
The DLV Project: A Tour from Theory and Research to Applications and Market
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Design and implementation of aggregate functions in the dlv system*
Theory and Practice of Logic Programming
On Reductive Semantics of Aggregates in Answer Set Programming
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Well-founded semantics for description logic programs in the semantic web
ACM Transactions on Computational Logic (TOCL)
First-Order encodings for modular nonmonotonic datalog programs
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
Unfounded sets and well-founded semantics of answer set programs with aggregates
Journal of Artificial Intelligence Research
Stepwise debugging of description-logic programs
Correct Reasoning
Exploiting unfounded sets for HEX-Program evaluation
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
Tableau Calculi for Logic Programs under Answer Set Semantics
ACM Transactions on Computational Logic (TOCL)
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Aggregates in answer set programming (ASP) have recently been studied quite intensively. The main focus of previous work has been on defining suitable semantics for programs with arbitrary, potentially recursive aggregates. By now, these efforts appear to have converged. On another line of research, the relation between unfounded sets and (aggregate-free) answer sets has lately been rediscovered. It turned out that most of the currently available answer set solvers rely on this or closely related results (e.g., loop formulas). In this paper, we unite these lines and give a new definition of unfounded sets for disjunctive logic programs with arbitrary, possibly recursive aggregates. While being syntactically somewhat different, we can show that this definition properly generalizes all main notions of unfounded sets that have previously been defined for fragments of the language. We demonstrate that, as for restricted languages, answer sets can be crisply characterized by unfounded sets: They are precisely the unfounded-free models. This result can be seen as a confirmation of the robustness of the definition of answer sets for arbitrary aggregates. We also provide a comprehensive complexity analysis for unfounded sets, and study its impact on answer set computation.